feat: add encoder tuning harness for 4K60 fractal videos

make_clips.sh renders lossless FFV1 4K60 test clips through the Makefile's
colour conversion; sweep.sh encodes them with a list of ffmpeg configs and
scores each with VMAF 4K (mean/p1/min), VMAF-NEG, CAMBI banding and PSNR-Y.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

.gitignore

@@ -1,3 +1,6 @@
 /target
 Cargo.lock
 dist
+frames*
+out.mp4
+__pycache__

CLAUDE.md

@@ -0,0 +1,333 @@
+# CLAUDE.md
+
+This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
+
+## What this is
+
+A deep-zoom fractal explorer (Rust + wgpu + egui + WGSL). It zooms past the
+~10¹³× limit of plain `f64` using **perturbation theory**: one high-precision
+reference orbit is computed on the CPU (arbitrary precision via `bignum::Big`:
+`rug` natively, `malachite-float` on the web),
+and every pixel is rendered on the GPU as a cheap `f32` delta from it, with
+rebasing to avoid glitches. Plain `f32` deltas run out of exponent range
+once a pixel is ~2^-124 wide (~10³⁴× at 1080p), so from 2^-122 per pixel
+(`view::DEEP_PIXEL_SIZE`) a `DEEP` shader variant starts each pixel with
+rescaled deltas (f32 mantissa × 2^i32). There's no practical depth limit:
+`half_height` is a `view::Scale` (f64 mantissa × 2^i32), floored only at
+`Scale::MIN` = 2^-(2^20) to keep shader exponent sums in i32. Runs
+natively (Vulkan/Metal/DX12) and in the browser (WebGPU only — WebGL2 can't do
+storage buffers, which the fragment shader needs for the reference orbit).
+
+## Commands
+
+```sh
+cargo run --release          # native, run (release matters: fractal math is hot)
+cargo test                   # reference-orbit math, share-link round-trip, WGSL validation
+cargo test --features wasm   # same, on the web build's malachite big-float backend
+cargo test --test shader_valid   # just the WGSL parse/validate tests (naga, no GPU needed)
+cargo clippy
+cargo fmt                    # rustfmt.toml just pins edition = "2024"
+cargo build --release --no-default-features   # headless-only binary: no eframe/egui (the default `gui` feature)
+tools/bench/bench.sh --rev HEAD   # perf of uncommitted edits vs HEAD (hyperfine; see tools/bench/README.md)
+```
+
+Web build (WebGPU):
+
+```sh
+rustup target add wasm32-unknown-unknown
+cargo install wasm-bindgen-cli --version 0.2.128   # must match the wasm-bindgen crate version
+./build-web.sh                                     # -> ./dist (builds with --features wasm)
+python3 -m http.server -d dist 8080
+```
+
+Native CLI flags (`src/cli.rs`, applied in `FractalApp::apply_cli`): `--kind`,
+`--power`, `--julia re,im`, `--phoenix-p re,im`, `--lambda-l re,im`,
+`--palette`, `--share <fragment>`,
+`--view re,im,half_height[,iterations]`, `--rendering-kind`,
+`--yaw`/`--pitch` (3D camera, degrees), `--de`, `--antialias` (2×2),
+`--buddhabrot`,
+`--buddha-palette`. `--headless` (`src/headless.rs`) skips the window
+entirely: it builds the same view from the other flags, creates its own
+offscreen wgpu device, and renders straight to a PNG (`--width`/`--height`,
+default 1920×1080, `--export-path out.png`) without needing a GPU-backed
+window/event loop. Not yet supported with `--buddhabrot`. Run
+`mandelbrot --help` for the full list.
+
+`--headless` also has an animation mode, for feeding into `ffmpeg`: give any
+end-state flag alongside the start flags (`--view`/`--share`/`--kind`/
+`--julia`/...), plus `--frames N` or `--fps`/`--duration`. End-state flags:
+`--to-view re,im,half_height[,iterations]` or `--to-share <fragment>` (only
+position/zoom/iterations are pulled out of the link), `--to-iterations`,
+`--to-julia`, `--to-phoenix-p`, `--to-lambda-l`, `--to-complex-power`
+(or `--to-complex-power-re`/`--to-complex-power-im` to move one component),
+and `--to-kind` (per-step formula blend via `KindMorph`, camera untouched).
+Anything without a target stays at its start value; colors stay fixed.
+`--export-path` then names an output *directory* of `frame-00001.png`,
+`frame-00002.png`, ... instead of a single file. `--export-path -` writes
+to stdout instead (refused on a terminal): the PNG for a still, or for an
+animation raw RGBA8 frames in order (`unpad_rgba`, no PNG encode) for
+`ffmpeg -f rawvideo -pix_fmt rgba -s WxH -r FPS -i -`. A single writer
+thread reorders the frames. Its buffer is bounded by the orbit workers not
+starting a frame more than `window` past the last one written, not by
+blocking the writer, which could deadlock. `headless.rs::AnimTargets`
+collects the targets; the export pipeline is rebuilt only when the
+`PipelineKey` changes between frames (kind morph). `view::interpolate_view`
+does the camera: half-height geometrically (log-linear, since zoom spans many
+decades), center linearly through the complex plane at full `Big` precision;
+constants interpolate linearly. `--linear` swaps the default smoothstep
+easing for constant pacing. `--shards N --shard K` (1-based) renders only
+the K-th of N contiguous parts (`shard_range`), still timed against the whole
+animation (global `t`, global `frame-NNNNN.png` numbers; stdout streams just
+that part), so separately rendered clips join seamlessly. Without `--to-iterations` (or a share link's),
+iteration count auto-scales with zoom depth per frame (same
+`auto_iteration_count` the interactive app uses while zooming).
+`--to-yaw`/`--to-pitch` (degrees, from `--yaw`/`--pitch`, yaw unwrapped so
+`--to-yaw 720` is two turns) orbit the 3D camera with `--rendering-kind 3d`.
+Frames are pipelined across every core (`run_animation`): each frame's
+state is a pure function of `t` (`apply_frame`), so all frames'
+`FractalApp::reference_job`s are snapshotted up front and `RefJob::compute`d
+by a worker pool. The main thread renders them on the GPU as they arrive
+(out of order), and another pool PNG-encodes and writes them
+(`encode_png`, `Compression::Fast`). Channels are bounded. Once orbits and
+encoding are off the main thread, the GPU is usually the bottleneck.
+
+There's no GPU in most sandboxes: `cargo check`/`cargo test --test shader_valid`
+are the fast, headless way to validate a change. `cargo test` also runs but
+doesn't touch the GPU — the reference-orbit tests are pure CPU math (see
+below), and `shader_valid` parses/validates WGSL with `naga` statically instead
+of creating a pipeline.
+
+## Architecture
+
+### The perturbation pipeline (the core mechanism, spans several files)
+
+For a pixel at parameter `c = C_ref + dc`, its orbit is written as
+`y_n = X_n + e_n`, where `X_n` is the (shared, high-precision) reference orbit
+and `e_n` is a small `f32` delta. Whenever `|y_n| < |e_n|` (or the reference
+runs out), rebase: `e ← y_n − X_0`, restart the reference index at 0. This is
+what makes deep zoom cheap — one expensive high-precision orbit, then every
+pixel is a handful of `f32` complex multiplies.
+
+- `src/bignum/` — `Big`, the arbitrary-precision binary float, with one
+  backend per library behind the same inherent API + operators: `rug`
+  (GMP/MPFR, default, fastest, can't target wasm32) and `malachite-float`
+  (pure Rust, the `wasm` feature, required for the web build; a
+  `compile_error!` enforces it). Cargo features are additive, so rug is a
+  non-wasm32 target dependency and the backend is picked by
+  `cfg(feature = "wasm")`. Both follow the precision rule: a result has the
+  larger operand precision, rounded to nearest; shifts are exact. Malachite's
+  zero has no precision, so its wrapper stores `prec` alongside. Any new
+  `Big` operation must be added to both backends (`cargo test` and
+  `cargo test --features wasm` run the same tests on each).
+- `src/view.rs` — `ViewState`; center is arbitrary-precision `Big`
+  (re-exported as `view::Big`). The pixel scale (`half_height`) is a `Scale`, an f64
+  mantissa with its own i32 exponent, so it goes past f64's ~1e-308. Never
+  collapse it (or a center difference) to a plain `f64` on a path used at
+  depth. Rescale first: `Scale::scaled_f64(k)`, or shift the `Big` by
+  `-scale_exp` before `to_f64()`, as `dc_offset`/`drift_from` do.
+  `Display`/`FromStr` use scientific notation of any exponent (share links,
+  `--view`, the zoom field). Precision (bits) scales with zoom depth
+  (`precision_for`). `needs_deep` switches rendering to the deep pipeline
+  once a pixel of the full-resolution render is below `DEEP_PIXEL_SIZE`
+  (2^-122; the f32 path is exact down to 2^-124 with AA's quarter-pixel
+  offsets, measured, and the deep path is ~40% slower, so the switch is as
+  late as that allows). `deep_scale_exp` gives the scale exponent.
+  `make_uniforms(aspect, height_px)` takes that full-resolution height, the
+  same during the interaction-downscaled pass so the pipeline doesn't flip.
+- `src/fractal/kind.rs` — the `FractalKind` enum (Mandelbrot, Burning Ship,
+  Tricorn, Multibrot, Celtic, Perpendicular, Buffalo, Phoenix, Lambda,
+  Complex Multibrot) plus everything that only needs to switch on it:
+  `label`/`description`/`formula` (UI text), `share_tag`/`from_share_tag`
+  (share-link encoding), `default_set_view` (per-kind starting view), and the
+  `ALL` array used to enumerate every kind.
+- `src/fractal/reference.rs` — `compute_reference`/`compute_set_reference`:
+  iterate the chosen formula at high precision on the CPU, emitting `Z_n` as
+  `f32` pairs — that's the reference orbit the GPU perturbs from. At
+  precision ≤ `F64_MAX_PRECISION` (80 bits, i.e. shallow views) it takes a
+  plain-`f64` fast path (`compute_reference_f64`), so each kind's formula
+  exists twice in this file (f64 + `Big`) and both must stay in sync;
+  `f64_fast_path_matches_big` checks they agree. The result is a `RefOrbit`:
+  `points` plus a parallel `exps`. A point below 2^-100 (only possible on the
+  `Big` path) is stored as a normalized mantissa with its exponent in `exps`
+  (the true value is `points[n]·2^exps[n]`). That happens when the orbit
+  passes near 0 at a deep minibrot. `has_scaled()` then forces the deep
+  pipeline, the only one that reads `exps`. Requests are made with 1.5×
+  iteration headroom (`reference_iterations` in `app.rs`), so auto-iterations
+  creeping up during a zoom doesn't recompute the orbit every frame. The
+  interactive reference buffers start at 2^17 points and grow on demand
+  (`FractalRenderer::ensure_ref_capacity`) up to `MAX_REF_POINTS` (2^24, the
+  128 MiB WebGPU default binding size). That is also the hard iteration
+  ceiling (`app.rs::MAX_ITERATIONS`), because the shader treats an exhausted
+  reference as escaped. The UI slider only goes to 100k when dragged; typed
+  values can go higher.
+- `src/shaders/*.wgsl` — none of these are standalone WGSL modules; WGSL has
+  no `#include`, so each is compiled by concatenating plain-text fragments
+  with `concat!`/`include_str!` at the `create_shader_module` call site (see
+  `renderer.rs`, `buddhabrot.rs`, and `tests/shader_valid.rs`, which must
+  concatenate the same pieces to validate what actually gets built).
+  `common.wgsl` (fullscreen-triangle vertex helper, `cmul`/`cpow`, `KIND_*`
+  constants) is prepended to every shader. `iterate_uniforms.wgsl` (the
+  perturbation-pipeline `Uniforms` struct + `palette()`) is additionally
+  prepended to `mandelbrot.wgsl` and `colorize.wgsl`, which share that layout.
+  Because there's no namespacing, a definition must live in exactly one file
+  among those concatenated together for a given shader — don't redefine a
+  `common.wgsl`/`iterate_uniforms.wgsl` symbol locally.
+- `src/shaders/mandelbrot.wgsl` — the perturbation fragment shader. It is
+  **specialized per pipeline** through WGSL `override` constants (`KIND`,
+  `IS_JULIA`, `DE`), so the per-iteration kind/Julia/DE branches fold away at
+  pipeline creation. Read those constants in the shader, never `u.kind` /
+  `u.is_julia` / `u.de_coloring` (they're still uploaded for layout reasons).
+  `renderer.rs` builds one pipeline set per `PipelineKey` lazily on first
+  use, and `tests/shader_valid.rs` compiles every kind × Julia × DE × morph ×
+  deep variant to SPIR-V. So a new kind needs no pipeline-list change, only its `KIND_*`
+  constant. `buddhabrot.wgsl` does the same with its own `override KIND`.
+  Interior pixels exit early through **periodicity detection**. It uses
+  Brent-style checkpoints plus two guards: the cycle's multiplier must be
+  clearly attracting (`PERIOD_MAX_MULT2`), and the contracting return must
+  repeat in `PERIOD_CONFIRMATIONS` consecutive windows. Both guards are
+  needed: without them, exterior pixels at cusps and minibrot edges turned
+  black. Retune them only against f64 ground truth on such views. Each
+  window saves its iterate closest to the critical point, not the one at the
+  checkpoint. At an arbitrary phase the relative tolerance is far coarser
+  than a deep minibrot's scale, and a black disk surrounded the minibrot
+  (seen at ~1e-13 zoom). Phoenix is excluded (two-term map).
+  `advance_delta(z, e)` is the per-kind delta step (`z` = reference point,
+  `e` = current delta); the caller adds `step_add` (= `dc`) afterward — this
+  relies on `c` being additive in every current kind's formula (a kind where
+  it isn't, e.g. a rational map with `c` in a denominator, would need its own
+  step function that consumes `dc` internally instead, plus extra per-step
+  reference data since the orbit point alone wouldn't be enough to recover an
+  exact delta). `fprime(z)` is the derivative used for distance-estimation
+  (DE) shading; exact for holomorphic kinds, an approximation (`~2Z`) for the
+  abs-based ones. A `KIND_*` constant (from `common.wgsl`) must match the
+  matching `FractalKind` variant's discriminant exactly. The per-kind bodies
+  are `advance_delta_kind`/`fprime_kind`; `advance_delta`/`fprime` wrap them
+  to blend two kinds during the kind-switch morph (`u.morph_from`,
+  `u.morph_w`: each step is `(1-w)·f_kind + w·f_from`, mirrored on the CPU by
+  the `morph` argument of `compute_reference`, in both its f64 and `Big`
+  paths). The blend only exists in pipelines built with the `MORPH` override
+  (part of `PipelineKey`, on while `morph_w > 0`); those also skip periodicity
+  detection and the cardioid bypass. App side: `KindMorph` in
+  `app.rs`; the uniforms use the morph the *current reference* was built with
+  (`ref_morph`), not the live one, so orbit and delta formula never disagree.
+  **Deep views** (`DEEP` override, `u.scale_exp != 0`) handle zooms where
+  f32 deltas underflow. `make_uniforms` sets `scale_exp = E` (≈ log2 of the
+  half-height) and uploads `span`/`dc_offset` × 2^-E. The per-pixel `offset`
+  and `px` are therefore in units of 2^E. `iterate_sample` first runs a
+  **deep prologue**:
+  - The delta is carried as `w·2^sx` and the DE derivative as `v·2^sv`
+    (separate exponents, since they drift apart near the critical point).
+  - Each step goes through `advance_delta_scaled` →
+    `deep_step_kind` → `advance_delta_scaled_kind`. These return the step at
+    its own output scale `t`. Next to the critical point (X tiny or 0), the
+    linear term vanishes and the step's value is ~e^p, far below 2^sx.
+    `deep_step_kind` measures X and e in a common unit (the kinds are
+    p-homogeneous) and the loop moves `sx` there. Assuming the e² terms merely
+    flush when negligible was wrong exactly there: pixels near deep minibrots
+    lost their delta and followed the reference forever.
+  - Rebasing uses X at full range (`ref_fe`).
+  - Once `|e| > 2^DEEP_EXIT_LOG2` (and dzs is normal), the state converts to
+    f32 and the ordinary loop continues from the same `n`/`m`.
+  - Periodicity detection restarts after the prologue with a sentinel save,
+    because saving the hand-off `z` (an arbitrary phase) made exterior pixels
+    shadowing a periodic nucleus reference read as interior.
+
+  The deep path is exact at any depth: forcing it everywhere (raise
+  `DEEP_PIXEL_SIZE`, raise `DEEP_EXIT_LOG2` to about -8) must reproduce the
+  plain f32 renders on non-chaotic views. That's the check to rerun after
+  changing it. Known gaps: Lambda's critical point is 1/2, so its step keeps
+  the input scale. Lambda set mode's reference sits at the origin, so it
+  never reaches deep zooms anyway.
+- `src/fractal/renderer.rs` — `FractalRenderer` (wgpu pipelines, uniform +
+  storage buffers, bind groups), `Uniforms` (repr(C) layout that must match
+  the WGSL `Uniforms` struct field-for-field, including padding; it includes
+  CPU-precomputed data: `cm_coef`, the Complex Multibrot binomial
+  coefficients from `app.rs::complex_binomials`, `light_count` for the
+  packed `GpuLight` buffer from `lights.rs::gpu_lights`, and `scale_exp`,
+  the deep view scale), `ref_exp_buffer` (binding 3, `RefOrbit::exps`), and
+  `FractalCallback` (the `egui_wgpu::CallbackTrait` impl: `prepare()` uploads
+  changed buffers and decides whether to re-run the iterate pass, the cheap
+  colourise pass, or just blit the cached texture). Also `ExportRender`, a
+  self-contained tiled renderer used for PNG export off the UI thread.
+- `src/worker.rs` — native background thread for reference-orbit computation
+  (coalesces bursts of requests so a fast drag doesn't compute every
+  intermediate view). The wasm32 build computes inline instead (see the
+  `#[cfg(target_arch = "wasm32")]` branch in `app.rs::ensure_reference`) —
+  **any signature change to `compute_reference`/`compute_set_reference` or
+  `RefRequest`/`RefResult` must be applied to both call sites.**
+- `src/app.rs` — `FractalApp` (the egui app + all UI). Key methods:
+  `should_request`/`ensure_reference` (decide when the reference is stale and
+  dispatch/collect it), `make_uniforms` (assemble the per-frame `Uniforms`),
+  `tick_animations` (drives the interactive animations: colour cycle,
+auto-zoom, c/p/λ circle drift via `ConstOrbit`, per-component complex-power
+oscillation via `AxisOsc`, 3D camera orbit, kind cycling through
+`switch_kind`),
+  `default_view_for` (wraps `FractalKind::default_set_view`, adding the
+  kind-independent Julia case). `JULIA_PRESETS` and `SET_PRESETS` are sized as
+  `[T; FractalKind::<last variant> as usize + 1]` — adding a new `FractalKind`
+  means bumping both (and adding an empty `&[]` slot to each if the kind has
+  none), plus adding it to `FractalKind::ALL` in `kind.rs`.
+- `src/fractal/share.rs` — `ShareState`: encodes the full view (mode, kind,
+  full-precision decimal center, zoom, iterations, per-kind constants,
+  coloring) as a `#`-fragment URL for bookmarking/sharing deep-zoom locations.
+
+### Adding a new `FractalKind`
+
+Touches, in order: `kind.rs` (enum variant + `ALL` slot + `label`/
+`description`/`formula`/`share_tag`/`from_share_tag`/`default_set_view`
+arms), `reference.rs` (CPU iteration formula arm, and a test comparing
+against a naive `f64` iteration), `common.wgsl` (matching `KIND_*` const),
+`mandelbrot.wgsl` (matching `advance_delta`/`fprime` arms, plus the deep
+path's `advance_delta_scaled_kind` arm, its degree in `deep_step_kind` and,
+if not z²-like, a `deep_fprime` arm), `buddhabrot.wgsl`
+(matching arm in `advance()`, if the kind makes sense as a Buddhabrot),
+`renderer.rs` `Uniforms` (only if the kind needs a new per-kind constant,
+e.g. Phoenix's `phoenix_p`), `app.rs` (`JULIA_PRESETS`/`SET_PRESETS` slot,
+and optionally a UI control for its constant + an animation toggle,
+following the Phoenix/Lambda pattern). If `c` doesn't enter the formula
+additively (e.g. a rational map with `c` in a denominator), the
+`advance_delta`/`step_add` split doesn't work — that needs its own step
+function plus extra per-step reference data uploaded in a second GPU buffer
+alongside the orbit.
+
+### Buddhabrot is a separate pipeline
+
+`src/fractal/buddhabrot.rs` + `src/shaders/buddhabrot.wgsl` implement the
+Monte-Carlo orbit-density histogram. It does **not** use the perturbation/
+reference-orbit machinery: a Buddhabrot sample's orbit scatters across the
+whole image rather than staying in one pixel, so it's plain `f32` iteration
+from the live view (no deep zoom) via a compute pass that accumulates into a
+histogram buffer, tone-mapped by a fragment pass every frame. Its own
+`KIND_*` iteration formulas in `advance()` must be kept in sync with
+`reference.rs` by hand (there's no shared code path).
+
+### Two-pass render + caching (`renderer.rs`)
+
+The interactive path splits iteration (expensive, perturbation) from
+colourising (cheap, palette remap) into separate offscreen textures, so
+palette/color-scale/offset tweaks skip re-iteration entirely (`geom_differs`
+vs `color_differs` in `renderer.rs` decide which pass reruns). A frame where
+neither differs uploads and renders nothing and only blits. So any new
+uniform field must go into one of those two functions (or the lights
+comparison), or changing it won't redraw.
+
+AA is **adaptive** on the interactive path. `fs_data` always iterates 1
+sample per pixel. When AA is on, `fs_refine` reads that texture and runs the
+2×2 grid only on pixels whose 4-neighbours differ (interior/exterior edge, or
+`ci`/DE beyond `AA_CI_EPS`/`AA_DE_EPS`), copying the rest. Colourise then
+reads the refined texture. PNG export (`fs_color`) still supersamples every
+pixel, except in 3D: the raymarcher needs the whole height field, so a 3D
+`ExportRender` (`RaymarchExport`) runs the interactive chain instead, with
+its tiles iterating `fs_data` into its own data texture and the last tile adding
+refine + colourise into the target.
+
+The 3D view (`colorize.wgsl::ray_marching`) sphere-traces the DE height
+field straight from the data texture. It's cheap: rays start on the z = 0
+plane, and most hit within a few steps (about 4 on average). A min-height
+mip pyramid (quadtree height-field tracing) was tried and measured about 3×
+slower, because it needs about 12 costlier steps per ray. Don't reintroduce it.
+Orbiting the camera only re-runs the colourise pass, never iteration.
+
+While the user is actively panning/zooming, the app renders downscaled with
+AA off (`INTERACT_DOWNSCALE`) and snaps back to full resolution once input
+settles (`INTERACT_SETTLE`).

Cargo.toml

@@ -3,19 +3,34 @@ name = "mandelbrot"
 version = "0.1.0"
 edition = "2024"
 
+[features]
+default = ["gui"]
+# Windowed egui app. Without it only `--headless` rendering is built.
+gui = ["dep:eframe", "dep:egui"]
+# Pure-Rust big floats for the web build (`rug` needs GMP/MPFR, which can't
+# target wasm32). Required for wasm32, optional natively (to test that backend).
+wasm = ["dep:malachite-float", "dep:malachite-base"]
+
 [dependencies]
 bytemuck = { version = "1.25.2", features = ["derive"] }
-dashu-float = "0.6.0"
+eframe = { version = "0.36.2", default-features = false, features = ["wgpu", "default_fonts", "x11", "wayland", "accesskit"], optional = true }
-eframe = { version = "0.36.2", default-features = false, features = ["wgpu", "default_fonts", "x11", "wayland", "accesskit"] }
+egui = { version = "0.36.2", optional = true }
-egui = "0.36.2"
+ecolor = { version = "0.36.2", features = ["bytemuck"] }
-futures-channel = { version = "0.3.34", default-features = false, features = ["alloc", "std"] }
+wgpu = "30.0.1"
+glam = "0.33.8"
 log = "0.4.34"
 png = "0.18.1"
+malachite-float = { version = "0.12", optional = true }
+malachite-base = { version = "0.12", optional = true }
 
 [target.'cfg(not(target_arch = "wasm32"))'.dependencies]
 env_logger = "0.11.11"
+clap = { version = "4.5.51", features = ["derive"] }
+pollster = "1.0.1"
+rug = { version = "1.30.0", default-features = false, features = ["float", "std"] }
 
 [target.'cfg(target_arch = "wasm32")'.dependencies]
+futures-channel = { version = "0.3.34", default-features = false, features = ["alloc", "std"] }
 console_error_panic_hook = "0.1.7"
 console_log = "1.1.0"
 js-sys = "0.3.105"
@@ -26,8 +41,10 @@ web-sys = { version = "0.3.105", features = ["Window", "Location", "Url", "UrlSe
 # Release: optimize hard (fractal math is hot).
 [profile.release]
 opt-level = 3
+# codegen-units = 1
+debug = true
 
-# Dev: keep our own crate debuggable, but optimize dependencies (dashu, wgpu,
+# Dev: keep our own crate debuggable, but optimize dependencies (big floats, wgpu,
 # egui) so the explorer is actually interactive during development.
 [profile.dev]
 opt-level = 1
@@ -36,4 +53,4 @@ opt-level = 1
 opt-level = 3
 
 [dev-dependencies]
-naga = { version = "30", features = ["wgsl-in"] }
+naga = { version = "30", features = ["wgsl-in", "spv-out"] }

Makefile

@@ -0,0 +1,35 @@
+.PHONY: hevc-nvenc x265 av1
+
+FFMPEG=ffmpeg
+IN_FMT=rgba
+
+RESOLUTION=1920x1080
+FPS=60
+OUT=out.mp4
+
+FFMPEG_CMD=$(FFMPEG) -f rawvideo -pix_fmt $(IN_FMT) -s $(RESOLUTION) -framerate $(FPS) -i - -vf "scale=out_color_matrix=bt709:out_range=tv:flags=accurate_rnd+full_chroma_int+bitexact,format=p010le"
+
+hevc-nvenc:
+	$(FFMPEG_CMD) \
+		-c:v hevc_nvenc -preset p7 -tune hq -rc vbr -cq 14 -b:v 0 -maxrate 200M -bufsize 400M \
+		-profile:v main10 -pix_fmt p010le \
+		-spatial-aq 1 -aq-strength 6 -temporal-aq 1 \
+		-rc-lookahead 32 -bf 4 -b_ref_mode middle -multipass fullres \
+		-colorspace bt709 -color_primaries bt709 -color_trc bt709 -color_range tv \
+		-tag:v hvc1 -movflags +faststart \
+		$(OUT)
+
+x265:
+	$(FFMPEG_CMD) \
+		-c:v libx265 -crf 18 -preset medium -pix_fmt yuv420p10le \
+		-x265-params "aq-mode=3:no-sao=1" \
+		-colorspace bt709 -color_primaries bt709 -color_trc bt709 -color_range tv \
+		-tag:v hvc1 -movflags +faststart \
+		$(OUT)
+
+av1:
+	$(FFMPEG_CMD) \
+		-c:v libsvtav1 -crf 24 -preset 6 -pix_fmt yuv420p10le \
+		-svtav1-params "film-grain=0:enable-overlays=0" \
+		-colorspace bt709 -color_primaries bt709 -color_trc bt709 -color_range tv \
+		$(OUT)

README.md

@@ -3,7 +3,8 @@
 A fast, interactive deep-zoom fractal explorer — Mandelbrot and Julia sets —
 built with **Rust + wgpu + egui + WGSL**. It zooms far past the ~10¹³× limit of
 plain `f64` using **perturbation theory**: one high-precision reference orbit is
-computed on the CPU (arbitrary precision via `dashu-float`), and every pixel is
+computed on the CPU (arbitrary precision via `rug` natively, `malachite-float`
+on the web), and every pixel is
 rendered on the GPU as a cheap `f32` delta from it, with **rebasing** to avoid
 glitches. Runs natively (Vulkan/Metal/DX12) and in the browser (WebGPU).
 
@@ -27,6 +28,9 @@ The `f32` GPU tier reaches roughly **10³⁰× magnification** with sharp detail
 cargo run --release
 ```
 
+Native builds use `rug` (GMP/MPFR) for the reference orbit, which needs a C
+toolchain and `m4` (on Windows, MSYS2).
+
 ## Build & run — web (WebGPU)
 
 Requires the `wasm32-unknown-unknown` target and `wasm-bindgen-cli` (matching the
@@ -37,6 +41,7 @@ rustup target add wasm32-unknown-unknown
 cargo install wasm-bindgen-cli --version 0.2.128   # once
 
 ./build-web.sh                       # outputs ./dist (index.html, .js, .wasm)
+                                     # (builds with --features wasm: pure-Rust big floats)
 python3 -m http.server -d dist 8080  # serve over http
 ```
 
@@ -60,7 +65,8 @@ qualifies. Deploy by serving the `dist/` directory as static files.
 
 ## How it works
 
-- `src/view.rs` — view state. Center is arbitrary precision (`FBig`); the pixel
+- `src/view.rs` — view state. Center is arbitrary precision (`Big`, from
+  `src/bignum/`); the pixel
   scale stays `f64` (even at 10³⁰× it is ~10⁻³³, within `f64` range).
 - `src/fractal/reference.rs` — high-precision reference orbit `Z_{n+1}=Z_n²+C`.
 - `src/shaders/mandelbrot.wgsl` — per-pixel perturbation `e_{n+1}=2·Z_n·e_n+e_n²+δc`
@@ -84,6 +90,7 @@ reference computation to a Web Worker.
 
 ```sh
 cargo test
+cargo test --features wasm   # same suite on the web build's big-float backend
 ```
 
 Covers the reference orbit (vs. a naive `f64` iteration, Mandelbrot and Julia)

build-web.sh

@@ -8,7 +8,7 @@ export PATH="$HOME/.cargo/bin:$PATH"
 OUT="${1:-dist}"
 
 echo "==> cargo build (wasm32, release)"
-cargo build --release --target wasm32-unknown-unknown
+cargo build --release --target wasm32-unknown-unknown --features wasm
 
 echo "==> wasm-bindgen -> $OUT"
 mkdir -p "$OUT"
@@ -20,6 +20,7 @@ wasm-bindgen \
     target/wasm32-unknown-unknown/release/mandelbrot.wasm
 
 cp index.html "$OUT/index.html"
+cp favicon.ico "$OUT/favicon.ico"
 
 echo "==> done: $OUT/ (index.html, mandelbrot.js, mandelbrot_bg.wasm)"
 echo "    serve:  python3 -m http.server -d $OUT 8080"

src/bignum/mod.rs

@@ -0,0 +1,225 @@
+//! Arbitrary-precision binary float [`Big`] (one coordinate of a deep-zoom
+//! center, or of a reference orbit point), over one of two backends:
+//!
+//! - native (default): `rug` (GMP/MPFR), the fastest, but C code that can't
+//!   target `wasm32-unknown-unknown`;
+//! - `wasm` feature: a pure-Rust library, required for the web build.
+//!
+//! Both expose the same inherent API plus the operators below, and follow
+//! the same precision rule: an operation's result has the larger of its
+//! operands' precisions (in bits), rounded to nearest. Shifts (`<<`/`>>` by
+//! an `isize`) are exact multiplications by powers of two.
+
+#[cfg(not(feature = "wasm"))]
+mod rug_backend;
+#[cfg(not(feature = "wasm"))]
+pub use rug_backend::Big;
+
+#[cfg(feature = "wasm")]
+mod web_backend;
+#[cfg(feature = "wasm")]
+pub use web_backend::Big;
+// Native `--features wasm` builds (to test the web backend) still link rug.
+#[cfg(all(feature = "wasm", not(target_arch = "wasm32")))]
+use rug as _;
+
+#[cfg(all(target_arch = "wasm32", not(feature = "wasm")))]
+compile_error!("the web build needs `--features wasm` (rug can't target wasm32)");
+
+use core::ops::{Add, Mul, Neg, Shl, Shr, Sub};
+
+/// Implements `$Trait` for every owned/borrowed combination of `Big`
+/// operands, through the backend's by-reference `$imp`.
+macro_rules! forward_binop {
+    ($Trait:ident, $method:ident, $imp:ident) => {
+        impl $Trait<&Big> for &Big {
+            type Output = Big;
+            fn $method(self, rhs: &Big) -> Big {
+                self.$imp(rhs)
+            }
+        }
+        impl $Trait<Big> for &Big {
+            type Output = Big;
+            fn $method(self, rhs: Big) -> Big {
+                self.$imp(&rhs)
+            }
+        }
+        impl $Trait<&Big> for Big {
+            type Output = Big;
+            fn $method(self, rhs: &Big) -> Big {
+                (&self).$imp(rhs)
+            }
+        }
+        impl $Trait<Big> for Big {
+            type Output = Big;
+            fn $method(self, rhs: Big) -> Big {
+                (&self).$imp(&rhs)
+            }
+        }
+    };
+}
+
+forward_binop!(Add, add, add_ref);
+forward_binop!(Sub, sub, sub_ref);
+forward_binop!(Mul, mul, mul_ref);
+
+impl Neg for Big {
+    type Output = Big;
+    fn neg(self) -> Big {
+        self.negated()
+    }
+}
+
+impl Neg for &Big {
+    type Output = Big;
+    fn neg(self) -> Big {
+        self.clone().negated()
+    }
+}
+
+impl Shl<isize> for Big {
+    type Output = Big;
+    fn shl(self, k: isize) -> Big {
+        self.mul_pow2(k)
+    }
+}
+
+impl Shl<isize> for &Big {
+    type Output = Big;
+    fn shl(self, k: isize) -> Big {
+        self.clone().mul_pow2(k)
+    }
+}
+
+impl Shr<isize> for Big {
+    type Output = Big;
+    fn shr(self, k: isize) -> Big {
+        self.mul_pow2(-k)
+    }
+}
+
+impl Shr<isize> for &Big {
+    type Output = Big;
+    fn shr(self, k: isize) -> Big {
+        self.clone().mul_pow2(-k)
+    }
+}
+
+/// Significant decimal digits of a value, as a backend's
+/// `to_decimal_parts` returns them: the value is `±0.digits × 10^exp10`,
+/// `digits` has no trailing zeros, and it is empty for zero.
+pub struct DecimalParts {
+    pub negative: bool,
+    pub digits: String,
+    pub exp10: isize,
+}
+
+impl DecimalParts {
+    /// Build from a significand digit string (maybe with trailing zeros)
+    /// whose value is `0.digits × 10^exp10`.
+    fn new(negative: bool, digits: &str, exp10: isize) -> Self {
+        let digits = digits.trim_end_matches('0').to_string();
+        Self {
+            negative: negative && !digits.is_empty(),
+            digits,
+            exp10,
+        }
+    }
+}
+
+impl Big {
+    /// Decimal string with `sig_digits` significant digits, in plain
+    /// positional notation (`-0.000123`, `4500`), trailing zeros trimmed.
+    pub fn to_decimal_string(&self, sig_digits: usize) -> String {
+        let DecimalParts {
+            negative,
+            digits,
+            exp10,
+        } = self.to_decimal_parts(sig_digits.max(1));
+        if digits.is_empty() {
+            return "0".to_string();
+        }
+        let sign = if negative { "-" } else { "" };
+        let len = digits.len() as isize;
+        if exp10 <= 0 {
+            let zeros = "0".repeat((-exp10) as usize);
+            format!("{sign}0.{zeros}{digits}")
+        } else if exp10 >= len {
+            let zeros = "0".repeat((exp10 - len) as usize);
+            format!("{sign}{digits}{zeros}")
+        } else {
+            let (int, frac) = digits.split_at(exp10 as usize);
+            format!("{sign}{int}.{frac}")
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn big(x: f64) -> Big {
+        Big::from_f64(x, 200)
+    }
+
+    #[test]
+    fn decimal_string_is_positional() {
+        assert_eq!(
+            big(-0.7515).to_decimal_string(20),
+            "-0.75149999999999994582"
+        );
+        assert_eq!(big(-0.7515).to_decimal_string(5), "-0.7515");
+        assert_eq!(big(0.0).to_decimal_string(5), "0");
+        assert_eq!(big(1.0).to_decimal_string(5), "1");
+        assert_eq!(big(123.456).to_decimal_string(5), "123.46");
+        assert_eq!(big(1e20).to_decimal_string(5), "100000000000000000000");
+        assert_eq!(big(0.1).to_decimal_string(5), "0.1");
+        let tiny = big(1.0) >> 200;
+        let s = tiny.to_decimal_string(5);
+        assert_eq!(s, format!("0.{}6223", "0".repeat(60)));
+    }
+
+    #[test]
+    fn decimal_round_trip() {
+        let s = "-0.743643887037158704752191506114774";
+        let x = Big::from_decimal_str(s, 200).unwrap();
+        assert_eq!(x.to_decimal_string(33), s);
+        assert_eq!(
+            Big::from_decimal_str("1.5e-20", 64).unwrap().to_f64(),
+            1.5e-20
+        );
+        assert!(Big::from_decimal_str("abc", 64).is_none());
+    }
+
+    #[test]
+    fn precision_is_max_of_operands() {
+        let a = Big::from_f64(1.0, 100);
+        let b = Big::from_f64(3.0, 200);
+        assert_eq!((&a + &b).precision(), 200);
+        assert_eq!((&a * &b).precision(), 200);
+        assert_eq!((&b - &a).precision(), 200);
+        assert_eq!(a.clone().with_precision(300).precision(), 300);
+    }
+
+    #[test]
+    fn exact_shifts_and_log2() {
+        let x = Big::from_f64(0.75, 64) >> 5000;
+        assert_eq!(x.log2_floor(), Some(-5001));
+        assert_eq!((x << 5000).to_f64(), 0.75);
+        assert_eq!(Big::zero(64).log2_floor(), None);
+        assert!(Big::from_f64(-1.0, 64).is_negative());
+        assert!(!Big::zero(64).is_negative());
+    }
+
+    #[test]
+    fn transcendentals() {
+        let x = Big::from_f64(0.5, 128);
+        assert!((x.ln().to_f64() - 0.5f64.ln()).abs() < 1e-15);
+        assert!((x.exp().to_f64() - 0.5f64.exp()).abs() < 1e-15);
+        let (s, c) = x.sin_cos();
+        assert!((s.to_f64() - 0.5f64.sin()).abs() < 1e-15);
+        assert!((c.to_f64() - 0.5f64.cos()).abs() < 1e-15);
+        let y = Big::from_f64(-0.3, 128);
+        assert!((y.atan2(&x).to_f64() - (-0.3f64).atan2(0.5)).abs() < 1e-15);
+    }
+}

src/bignum/rug_backend.rs

@@ -0,0 +1,128 @@
+//! [`Big`] over `rug::Float` (MPFR), for native builds.
+
+use core::cmp::Ordering;
+
+use rug::{Assign, Float};
+
+use super::DecimalParts;
+
+/// Arbitrary-precision binary float. See the module docs.
+#[derive(Clone, Debug, PartialEq)]
+pub struct Big(Float);
+
+/// MPFR precision for `bits`, clamped to what it accepts.
+fn prec(bits: usize) -> u32 {
+    (bits as u32).clamp(rug::float::prec_min(), rug::float::prec_max())
+}
+
+impl Big {
+    /// `x` at `bits` of precision (exact when `bits >= 53`). Non-finite `x`
+    /// reads as 0.
+    pub fn from_f64(x: f64, bits: usize) -> Self {
+        let x = if x.is_finite() { x } else { 0.0 };
+        Self(Float::with_val(prec(bits), x))
+    }
+
+    pub fn zero(bits: usize) -> Self {
+        Self(Float::new(prec(bits)))
+    }
+
+    /// Parse a decimal (`-0.75`, `1.5e-20`, any number of digits) at `bits`
+    /// (at least 53) of precision.
+    pub fn from_decimal_str(s: &str, bits: usize) -> Option<Self> {
+        let parsed = Float::parse(s.trim()).ok()?;
+        let x = Float::with_val(prec(bits.max(53)), parsed);
+        x.is_finite().then_some(Self(x))
+    }
+
+    pub fn precision(&self) -> usize {
+        self.0.prec() as usize
+    }
+
+    /// Change the precision, rounding to nearest if it shrinks.
+    pub fn with_precision(mut self, bits: usize) -> Self {
+        self.0.set_prec(prec(bits));
+        self
+    }
+
+    pub fn to_f64(&self) -> f64 {
+        self.0.to_f64()
+    }
+
+    pub fn is_zero(&self) -> bool {
+        self.0.is_zero()
+    }
+
+    pub fn is_negative(&self) -> bool {
+        self.0.cmp0() == Some(Ordering::Less)
+    }
+
+    pub fn abs(self) -> Self {
+        Self(self.0.abs())
+    }
+
+    pub fn sqr(&self) -> Self {
+        Self(Float::with_val(self.0.prec(), self.0.square_ref()))
+    }
+
+    /// `floor(log2|x|)`, or `None` for zero. Exact, at any exponent.
+    pub fn log2_floor(&self) -> Option<isize> {
+        // MPFR normalizes the significand to [0.5, 1).
+        self.0.get_exp().map(|e| e as isize - 1)
+    }
+
+    pub fn ln(&self) -> Self {
+        Self(Float::with_val(self.0.prec(), self.0.ln_ref()))
+    }
+
+    pub fn exp(&self) -> Self {
+        Self(Float::with_val(self.0.prec(), self.0.exp_ref()))
+    }
+
+    /// `atan2(self, x)`: the angle of `(x, self)`.
+    pub fn atan2(&self, x: &Big) -> Self {
+        let p = self.0.prec().max(x.0.prec());
+        Self(Float::with_val(p, self.0.atan2_ref(&x.0)))
+    }
+
+    pub fn sin_cos(&self) -> (Self, Self) {
+        let p = self.0.prec();
+        let (mut s, mut c) = (Float::new(p), Float::new(p));
+        (&mut s, &mut c).assign(self.0.sin_cos_ref());
+        (Self(s), Self(c))
+    }
+
+    /// `sig` significant decimal digits (rounded to nearest).
+    pub fn to_decimal_parts(&self, sig: usize) -> DecimalParts {
+        if self.0.is_zero() {
+            return DecimalParts::new(false, "", 0);
+        }
+        let (negative, digits, exp) = self.0.to_sign_string_exp(10, Some(sig));
+        DecimalParts::new(negative, &digits, exp.unwrap_or(0) as isize)
+    }
+
+    pub(super) fn add_ref(&self, rhs: &Big) -> Big {
+        let p = self.0.prec().max(rhs.0.prec());
+        Big(Float::with_val(p, &self.0 + &rhs.0))
+    }
+
+    pub(super) fn sub_ref(&self, rhs: &Big) -> Big {
+        let p = self.0.prec().max(rhs.0.prec());
+        Big(Float::with_val(p, &self.0 - &rhs.0))
+    }
+
+    pub(super) fn mul_ref(&self, rhs: &Big) -> Big {
+        let p = self.0.prec().max(rhs.0.prec());
+        Big(Float::with_val(p, &self.0 * &rhs.0))
+    }
+
+    pub(super) fn negated(self) -> Big {
+        Big(-self.0)
+    }
+
+    /// `self · 2^k`, exact. `|k|` stays far below `i32::MAX` (precision and
+    /// zoom depth are capped around 2^20 bits).
+    pub(super) fn mul_pow2(self, k: isize) -> Big {
+        Big(self.0 << k as i32)
+    }
+}

src/bignum/web_backend.rs

@@ -0,0 +1,173 @@
+//! [`Big`] over `malachite-float`, pure Rust, for the web build.
+
+use malachite_base::num::basic::traits::Zero;
+use malachite_base::num::conversion::string::options::ToSciOptions;
+use malachite_base::num::conversion::traits::{RoundingFrom, ToSci};
+use malachite_base::rounding_modes::RoundingMode::Nearest;
+use malachite_float::Float;
+
+use super::DecimalParts;
+
+/// Arbitrary-precision binary float. See the module docs.
+///
+/// The precision is stored next to the value: malachite's zero has none,
+/// but "zero at `p` bits" must still lift a sum with it to `p` bits.
+#[derive(Clone, Debug)]
+pub struct Big {
+    f: Float,
+    prec: u64,
+}
+
+impl PartialEq for Big {
+    fn eq(&self, other: &Self) -> bool {
+        self.f == other.f
+    }
+}
+
+fn prec(bits: usize) -> u64 {
+    (bits as u64).max(1)
+}
+
+impl Big {
+    fn new(f: Float, prec: u64) -> Self {
+        // Only finite values reach here; anything else (overflow) is a bug.
+        debug_assert!(f.is_finite(), "non-finite Big: {f}");
+        Self { f, prec }
+    }
+
+    /// `x` at `bits` of precision (exact when `bits >= 53`). Non-finite `x`
+    /// reads as 0.
+    pub fn from_f64(x: f64, bits: usize) -> Self {
+        let p = prec(bits);
+        if !x.is_finite() {
+            return Self::zero(bits);
+        }
+        Self::new(Float::from_primitive_float_prec(x, p).0, p)
+    }
+
+    pub fn zero(bits: usize) -> Self {
+        Self::new(Float::ZERO, prec(bits))
+    }
+
+    /// Parse a decimal (`-0.75`, `1.5e-20`, any number of digits) at `bits`
+    /// (at least 53) of precision.
+    pub fn from_decimal_str(s: &str, bits: usize) -> Option<Self> {
+        let p = prec(bits.max(53));
+        let (f, _) = Float::from_sci_string_prec(s.trim(), p)?;
+        f.is_finite().then(|| Self::new(f, p))
+    }
+
+    pub fn precision(&self) -> usize {
+        self.prec as usize
+    }
+
+    /// Change the precision, rounding to nearest if it shrinks.
+    pub fn with_precision(mut self, bits: usize) -> Self {
+        let p = prec(bits);
+        if self.f.get_prec().is_some() {
+            self.f.set_prec(p);
+        }
+        self.prec = p;
+        self
+    }
+
+    pub fn to_f64(&self) -> f64 {
+        f64::rounding_from(&self.f, Nearest).0
+    }
+
+    pub fn is_zero(&self) -> bool {
+        self.f.is_zero()
+    }
+
+    pub fn is_negative(&self) -> bool {
+        self.f.is_sign_negative() && !self.f.is_zero()
+    }
+
+    pub fn abs(self) -> Self {
+        if self.f.is_sign_negative() {
+            self.negated()
+        } else {
+            self
+        }
+    }
+
+    pub fn sqr(&self) -> Self {
+        Self::new(self.f.square_prec_ref(self.prec).0, self.prec)
+    }
+
+    /// `floor(log2|x|)`, or `None` for zero. Exact, at any exponent.
+    pub fn log2_floor(&self) -> Option<isize> {
+        // The significand is normalized to [0.5, 1).
+        self.f.get_exponent().map(|e| e as isize - 1)
+    }
+
+    pub fn ln(&self) -> Self {
+        Self::new(self.f.ln_prec_ref(self.prec).0, self.prec)
+    }
+
+    pub fn exp(&self) -> Self {
+        Self::new(self.f.exp_prec_ref(self.prec).0, self.prec)
+    }
+
+    /// `atan2(self, x)`: the angle of `(x, self)`.
+    pub fn atan2(&self, x: &Big) -> Self {
+        let p = self.prec.max(x.prec);
+        Self::new(self.f.atan2_prec_ref_ref(&x.f, p).0, p)
+    }
+
+    pub fn sin_cos(&self) -> (Self, Self) {
+        let (s, c, _, _) = self.f.sin_cos_prec_ref(self.prec);
+        (Self::new(s, self.prec), Self::new(c, self.prec))
+    }
+
+    /// `sig` significant decimal digits (rounded to nearest).
+    pub fn to_decimal_parts(&self, sig: usize) -> DecimalParts {
+        if self.f.is_zero() {
+            return DecimalParts::new(false, "", 0);
+        }
+        let mut options = ToSciOptions::default();
+        options.set_precision(sig as u64);
+        let s = self.f.to_sci_with_options(options).to_string();
+        // `[-]int[.frac][e±N]`, positional or scientific depending on size.
+        let (negative, s) = match s.strip_prefix('-') {
+            Some(rest) => (true, rest),
+            None => (false, s.as_str()),
+        };
+        let (mantissa, exp) = match s.split_once(['e', 'E']) {
+            Some((m, e)) => (m, e.trim_start_matches('+').parse::<isize>().unwrap_or(0)),
+            None => (s, 0),
+        };
+        let (int, frac) = mantissa.split_once('.').unwrap_or((mantissa, ""));
+        let all = format!("{int}{frac}");
+        let digits = all.trim_start_matches('0');
+        let leading_zeros = (all.len() - digits.len()) as isize;
+        // 0.digits · 10^exp10 = int.frac · 10^exp.
+        let exp10 = int.len() as isize - leading_zeros + exp;
+        DecimalParts::new(negative, digits, exp10)
+    }
+
+    pub(super) fn add_ref(&self, rhs: &Big) -> Big {
+        let p = self.prec.max(rhs.prec);
+        Big::new(self.f.add_prec_ref_ref(&rhs.f, p).0, p)
+    }
+
+    pub(super) fn sub_ref(&self, rhs: &Big) -> Big {
+        let p = self.prec.max(rhs.prec);
+        Big::new(self.f.sub_prec_ref_ref(&rhs.f, p).0, p)
+    }
+
+    pub(super) fn mul_ref(&self, rhs: &Big) -> Big {
+        let p = self.prec.max(rhs.prec);
+        Big::new(self.f.mul_prec_ref_ref(&rhs.f, p).0, p)
+    }
+
+    pub(super) fn negated(self) -> Big {
+        Big::new(-self.f, self.prec)
+    }
+
+    /// `self · 2^k`, exact (malachite's exponent range is ±2^30, far past
+    /// what zoom depth needs).
+    pub(super) fn mul_pow2(self, k: isize) -> Big {
+        Big::new(self.f << k as i64, self.prec)
+    }
+}

src/camera.rs

@@ -0,0 +1,91 @@
+use std::f32::consts::{PI, TAU};
+
+use glam::Vec3;
+
+/// Pitch is kept just short of straight up/down so the view never flips past
+/// the pole (and the raymarcher's rays always have `z > 0`).
+const PITCH_LIMIT: f32 = PI / 2.0 - 0.01;
+
+#[derive(Default, Clone)]
+pub struct Camera {
+    pub position: glam::Vec3,
+
+    pub yaw: f32,
+    pub pitch: f32,
+
+    pub aspect_ratio: f32,
+    z_near: f32,
+    z_far: f32,
+}
+
+impl Camera {
+    pub fn new() -> Self {
+        Self {
+            position: Vec3::new(0., 0., -1.),
+            yaw: 0. * PI / 180.,
+            pitch: -30. * PI / 180.,
+            aspect_ratio: 1.,
+            z_near: 0.1,
+            z_far: 100.,
+        }
+    }
+
+    pub fn set_aspect_ratio(&mut self, aspect_ratio: f32) {
+        self.aspect_ratio = aspect_ratio;
+    }
+
+    /// Adjust yaw/pitch by the given deltas (radians). Pitch is clamped just
+    /// short of straight up/down to avoid the view flipping past the pole.
+    /// Yaw is wrapped to [-π, π) so the 2D <-> 3D transition (which scales
+    /// yaw by `t`) always unwinds the short way instead of every past turn.
+    pub fn rotate(&mut self, dyaw: f32, dpitch: f32) {
+        self.yaw = (self.yaw + dyaw + PI).rem_euclid(TAU) - PI;
+        self.pitch = (self.pitch + dpitch).clamp(-PITCH_LIMIT, PITCH_LIMIT);
+    }
+
+    /// Set yaw/pitch (radians) outright. Pitch is clamped as in `rotate`,
+    /// but yaw is left unwrapped: only a camera that stays in 3D (headless
+    /// animation, which interpolates yaw across several turns) should use
+    /// this; `rotate(0., 0.)` afterwards wraps it for the 2D <-> 3D transition.
+    #[cfg(not(target_arch = "wasm32"))]
+    pub fn set_angles(&mut self, yaw: f32, pitch: f32) {
+        self.yaw = yaw;
+        self.pitch = pitch.clamp(-PITCH_LIMIT, PITCH_LIMIT);
+    }
+
+    /// `render_scale` is the 3D texture's per-axis scale (see
+    /// `FractalApp::render_scale_3d`): the full 3D camera (`t = 1`) zooms in
+    /// by the same factor, so one texel still covers one screen pixel and the
+    /// extra texels become terrain beyond the screen edges.
+    pub fn orthographic(&self, t: f32, render_scale: f32) -> glam::Mat4 {
+        let yaw = self.yaw * t;
+        let pitch = self.pitch * t;
+
+        let zoom = 0.5 * (1. + t * (render_scale - 1.));
+        // Orbit pivot: the center of the fractal texture, which the raymarcher's
+        // `sdf` lays out over world x ∈ [0, aspect], y ∈ [0, 1] on the z = 0 plane.
+        let view = glam::Mat4::from_translation(Vec3::new(0.5 * self.aspect_ratio, 0.5, 0.))
+            * glam::Mat4::from_rotation_z(-yaw)
+            * glam::Mat4::from_rotation_x(-pitch)
+            * glam::Mat4::from_translation(self.position);
+
+        glam::camera::lh::proj::directx::orthographic(
+            -self.aspect_ratio / 4. / zoom,
+            self.aspect_ratio / 4. / zoom,
+            -0.25 / zoom,
+            0.25 / zoom,
+            self.z_near,
+            self.z_far,
+        ) * view.inverse()
+    }
+
+    pub fn direction(&self, t: f32) -> glam::Vec3 {
+        let yaw = self.yaw * t;
+        let pitch = self.pitch * t;
+
+        let forward =
+            glam::Mat3::from_rotation_z(-yaw) * glam::Mat3::from_rotation_x(-pitch) * glam::Vec3::Z;
+
+        forward.normalize()
+    }
+}

src/cli.rs

@@ -0,0 +1,243 @@
+// Native command-line arguments. Currently mirrors the old `MANDEL_*` debug
+// env vars one-for-one; this is the foundation a future headless (no-window,
+// render-to-file) mode will build on.
+
+use clap::{Parser, ValueEnum};
+
+use crate::fractal::FractalKind;
+
+#[derive(Parser, Debug, Default)]
+#[command(name = "mandelbrot", about = "Deep-zoom fractal explorer", version)]
+pub struct Cli {
+    /// Fractal formula to render.
+    #[arg(long, value_enum)]
+    pub kind: Option<KindArg>,
+
+    /// Start in Julia mode with this seed constant.
+    #[arg(long, value_name = "RE,IM")]
+    pub julia: Option<String>,
+
+    /// Switch to the Buddhabrot renderer.
+    #[arg(long)]
+    pub buddhabrot: bool,
+
+    /// Rendering mode to use.
+    #[arg(long)]
+    pub rendering_kind: Option<RenderingKindArg>,
+
+    /// Exponent for the Multibrot kind (z -> z^power + c), clamped to [2, 20].
+    #[arg(long)]
+    pub power: Option<u32>,
+
+    /// Complex exponent for the Complex Multibrot kind (z -> z^power + c).
+    #[arg(long, value_name = "RE,IM")]
+    pub complex_power: Option<String>,
+
+    /// Phoenix constant p for the Phoenix kind (z -> z^2 + c + p*z_prev).
+    #[arg(long, value_name = "RE,IM")]
+    pub phoenix_p: Option<String>,
+
+    /// Lambda constant λ for the Lambda kind (z -> λ*z*(1 - z)).
+    #[arg(long, value_name = "RE,IM")]
+    pub lambda_l: Option<String>,
+
+    /// Restore a view from a share-link fragment (the part after '#').
+    #[arg(long, value_name = "FRAGMENT")]
+    pub share: Option<String>,
+
+    /// Jump to a view on startup.
+    #[arg(long, value_name = "RE,IM,HALF_HEIGHT[,ITERATIONS]")]
+    pub view: Option<String>,
+
+    /// Jump to a specific position on startup.
+    #[arg(long, short('p'), value_name = "RE,IM")]
+    pub position: Option<String>,
+
+    /// Set a maximum iterations count on startup.
+    #[arg(long, short('i'))]
+    pub iterations: Option<u32>,
+
+    /// Set the zoom level on startup.
+    #[arg(long("zoom"), short('z'))]
+    pub half_height: Option<String>,
+
+    /// 3D camera yaw in degrees (with --rendering-kind 3d).
+    #[arg(long, value_name = "DEG", allow_hyphen_values = true)]
+    pub yaw: Option<f32>,
+
+    /// 3D camera pitch in degrees (with --rendering-kind 3d); negative tilts
+    /// the view down toward the fractal. Clamped short of ±90.
+    #[arg(long, value_name = "DEG", allow_hyphen_values = true)]
+    pub pitch: Option<f32>,
+
+    /// Enable distance-estimation shading.
+    #[arg(long)]
+    pub de: bool,
+
+    /// Enable 2×2 antialiasing (supersampling; ~4× slower).
+    #[arg(long)]
+    pub antialias: bool,
+
+    /// Coloring palette index.
+    #[arg(long, value_name = "INDEX")]
+    pub palette: Option<u32>,
+
+    /// Output path for --headless (default: fractal-<timestamp>.png). When
+    /// animating (--to-view/--to-share), this is a directory of
+    /// frame-00001.png, frame-00002.png, ... instead (default:
+    /// frames-<timestamp>/). "-" writes to stdout: the PNG for a single
+    /// image, or raw RGBA8 frames in order for an animation, to pipe into
+    /// `ffmpeg -f rawvideo -pix_fmt rgba -s WxH -r FPS -i - ...`.
+    #[arg(long, value_name = "PATH")]
+    pub export_path: Option<String>,
+
+    /// End view for an animation: "re,im,half_height[,iterations]", the same
+    /// syntax as --view. Combine with --view (or --share, --kind, --julia...)
+    /// for the start view; headless then renders a sequence of frames
+    /// interpolating the camera from start to end instead of a single PNG.
+    #[arg(long, value_name = "RE,IM,HALF_HEIGHT[,ITERATIONS]")]
+    pub to_view: Option<String>,
+
+    /// End view for an animation, as a share-link fragment (only the
+    /// position/zoom/iterations are used; alternative to --to-view for
+    /// pasting a location copied from the app's "Copy share link").
+    #[arg(long, value_name = "FRAGMENT")]
+    pub to_share: Option<String>,
+
+    /// Set a maximum iterations count at animation end.
+    #[arg(long)]
+    pub to_iterations: Option<u32>,
+
+    /// End Julia constant for an animation: c is interpolated from --julia
+    /// to this over the frames.
+    #[arg(long, value_name = "RE,IM", allow_hyphen_values = true)]
+    pub to_julia: Option<String>,
+
+    /// End Phoenix constant p for an animation (from --phoenix-p).
+    #[arg(long, value_name = "RE,IM", allow_hyphen_values = true)]
+    pub to_phoenix_p: Option<String>,
+
+    /// End Lambda constant λ for an animation (from --lambda-l).
+    #[arg(long, value_name = "RE,IM", allow_hyphen_values = true)]
+    pub to_lambda_l: Option<String>,
+
+    /// End Complex Multibrot exponent for an animation (from
+    /// --complex-power). Shorthand for --to-complex-power-re +
+    /// --to-complex-power-im.
+    #[arg(long, value_name = "RE,IM", allow_hyphen_values = true)]
+    pub to_complex_power: Option<String>,
+
+    /// End real part of the Complex Multibrot exponent for an animation;
+    /// the imaginary part stays put unless --to-complex-power-im is given.
+    #[arg(long, value_name = "RE", allow_hyphen_values = true)]
+    pub to_complex_power_re: Option<f64>,
+
+    /// End imaginary part of the Complex Multibrot exponent for an animation;
+    /// the real part stays put unless --to-complex-power-re is given.
+    #[arg(long, value_name = "IM", allow_hyphen_values = true)]
+    pub to_complex_power_im: Option<f64>,
+
+    /// End 3D camera yaw for an animation, in degrees (from --yaw). Not
+    /// wrapped: --yaw 0 --to-yaw 720 orbits twice.
+    #[arg(long, value_name = "DEG", allow_hyphen_values = true)]
+    pub to_yaw: Option<f32>,
+
+    /// End 3D camera pitch for an animation, in degrees (from --pitch).
+    #[arg(long, value_name = "DEG", allow_hyphen_values = true)]
+    pub to_pitch: Option<f32>,
+
+    /// Morph the iteration formula from the start kind (--kind) to this one
+    /// over the animation. The camera is unaffected (use --to-view for that).
+    #[arg(long, value_enum)]
+    pub to_kind: Option<KindArg>,
+
+    /// Number of frames to render for an animation. Alternative to --fps +
+    /// --duration.
+    #[arg(long, value_name = "N")]
+    pub frames: Option<u32>,
+
+    /// Frames per second, used with --duration to compute the frame count
+    /// (ignored if --frames is given). Also used in the ffmpeg command
+    /// hint printed after rendering.
+    #[arg(long, value_name = "N", default_value_t = 30.0)]
+    pub fps: f64,
+
+    /// Animation duration in seconds, used with --fps to compute the frame
+    /// count (ignored if --frames is given).
+    #[arg(long, value_name = "SECONDS")]
+    pub duration: Option<f64>,
+
+    /// Pace animation frames linearly instead of easing in/out (smoothstep).
+    #[arg(long)]
+    pub linear: bool,
+
+    /// Split the animation into N equal parts (use with --shard) to render
+    /// it across several runs. Each part keeps the whole animation's timing
+    /// and easing, so the clips join seamlessly.
+    #[arg(long, value_name = "N")]
+    pub shards: Option<u32>,
+
+    /// Which part of --shards to render, 1-based. PNG frames keep their
+    /// global numbering, so all shards can share one --export-path directory.
+    #[arg(long, value_name = "K")]
+    pub shard: Option<u32>,
+
+    /// Run without opening a window: render the current view to a PNG and
+    /// exit. Combine with --kind/--julia/--share/--view etc. to pick what to
+    /// render, or any --to-* flag (--to-view, --to-julia, --to-kind, ...) to
+    /// render an animation instead of a single frame. Not yet supported with --buddhabrot.
+    #[arg(long)]
+    pub headless: bool,
+
+    /// Output image width in pixels (--headless only).
+    #[arg(long, value_name = "PX", default_value_t = 1920)]
+    pub width: u32,
+
+    /// Output image height in pixels (--headless only).
+    #[arg(long, value_name = "PX", default_value_t = 1080)]
+    pub height: u32,
+}
+
+#[derive(Copy, Clone, Debug, ValueEnum)]
+pub enum KindArg {
+    Mandelbrot,
+    #[value(alias = "ship")]
+    BurningShip,
+    #[value(alias = "mandelbar")]
+    Tricorn,
+    #[value(alias = "multi")]
+    Multibrot,
+    Celtic,
+    #[value(alias = "perp")]
+    Perpendicular,
+    Buffalo,
+    Phoenix,
+    Lambda,
+    #[value(alias = "cmulti")]
+    ComplexMultibrot,
+}
+
+#[derive(Copy, Clone, Debug, ValueEnum)]
+pub enum RenderingKindArg {
+    Classic,
+    Shadow,
+    #[value(alias = "3d")]
+    Dimension3,
+}
+
+impl From<KindArg> for FractalKind {
+    fn from(k: KindArg) -> Self {
+        match k {
+            KindArg::Mandelbrot => FractalKind::Mandelbrot,
+            KindArg::BurningShip => FractalKind::BurningShip,
+            KindArg::Tricorn => FractalKind::Tricorn,
+            KindArg::Multibrot => FractalKind::Multibrot,
+            KindArg::Celtic => FractalKind::Celtic,
+            KindArg::Perpendicular => FractalKind::Perpendicular,
+            KindArg::Buffalo => FractalKind::Buffalo,
+            KindArg::Phoenix => FractalKind::Phoenix,
+            KindArg::Lambda => FractalKind::Lambda,
+            KindArg::ComplexMultibrot => FractalKind::ComplexMultibrot,
+        }
+    }
+}

src/fractal/buddhabrot.rs

@@ -0,0 +1,419 @@
+//! Buddhabrot / Nebulabrot rendering: a Monte-Carlo orbit-density histogram,
+//! accumulated progressively across frames by a compute pass and tone-mapped
+//! to colour by a fragment pass. See `shaders/buddhabrot.wgsl` for the "why"
+//! this is a separate pipeline from the escape-time perturbation renderer.
+
+use std::collections::HashMap;
+
+#[cfg(feature = "gui")]
+use eframe::egui_wgpu;
+
+/// Random samples dispatched per accumulating frame. Chosen so a frame stays
+/// interactive on a modest GPU even when most samples run the full `b_cap`
+/// (e.g. the view sits entirely inside the set, so nothing escapes).
+const SAMPLES_PER_DISPATCH: u32 = 150_000;
+const WORKGROUP_SIZE: u32 = 64;
+
+/// GPU-side parameters for both the accumulate (compute) and tonemap
+/// (fragment) passes. Layout must match `Uniforms` in `buddhabrot.wgsl`.
+#[repr(C)]
+#[derive(Copy, Clone, PartialEq, bytemuck::Pod, bytemuck::Zeroable)]
+pub struct BuddhabrotUniforms {
+    pub center: [f32; 2],
+    pub half_height: f32,
+    pub aspect: f32,
+    pub phoenix_p: [f32; 2],
+    pub lambda_l: [f32; 2],
+    pub bailout_sq: f32,
+    /// Iteration formula (`FractalKind::shader_id`); `KIND_LAMBDA` samples z0
+    /// instead of c (see the shader's doc comment).
+    pub kind: u32,
+    /// Exponent for the Multibrot kind.
+    pub power: u32,
+    /// Nested escape-iteration caps (r_cap <= g_cap <= b_cap) that bucket an
+    /// orbit's points into the R/G/B histogram planes.
+    pub r_cap: u32,
+    pub g_cap: u32,
+    pub b_cap: u32,
+    /// RNG nonce, bumped every dispatch so each frame samples fresh points.
+    pub seed: u32,
+    pub samples_this_dispatch: u32,
+    /// Tonemap brightness multiplier (user-controlled).
+    pub exposure: f32,
+    pub width: u32,
+    pub height: u32,
+    /// Running total of samples accumulated into the current histogram
+    /// (across all dispatches since the last reset); normalizes brightness.
+    pub total_samples: f32,
+    /// Tonemap colour style: 0 = classic (R/G/B = raw caps), 1 = nebula
+    /// (yellow core, blue halo), 2 = grayscale. Display-only, like `exposure`
+    /// — excluded from `ContentKey` so changing it doesn't reset accumulation.
+    pub palette: u32,
+    /// Padding so `complex_power` (a vec2, 8-byte aligned in the shader)
+    /// starts on an 8-byte boundary.
+    pub _pad0: u32,
+    /// Complex exponent for the Complex Multibrot kind; ignored by other kinds.
+    pub complex_power: [f32; 2],
+}
+
+/// The subset of `BuddhabrotUniforms` that determines the *content* of the
+/// histogram (as opposed to `exposure`, a display-only rescale). A change in
+/// any of these invalidates the accumulated histogram.
+#[derive(Copy, Clone, PartialEq)]
+struct ContentKey {
+    center: [f32; 2],
+    half_height: f32,
+    aspect: f32,
+    phoenix_p: [f32; 2],
+    lambda_l: [f32; 2],
+    bailout_sq: f32,
+    kind: u32,
+    power: u32,
+    complex_power: [f32; 2],
+    r_cap: u32,
+    g_cap: u32,
+    b_cap: u32,
+}
+
+impl From<&BuddhabrotUniforms> for ContentKey {
+    fn from(u: &BuddhabrotUniforms) -> Self {
+        Self {
+            center: u.center,
+            half_height: u.half_height,
+            aspect: u.aspect,
+            phoenix_p: u.phoenix_p,
+            lambda_l: u.lambda_l,
+            bailout_sq: u.bailout_sq,
+            kind: u.kind,
+            power: u.power,
+            complex_power: u.complex_power,
+            r_cap: u.r_cap,
+            g_cap: u.g_cap,
+            b_cap: u.b_cap,
+        }
+    }
+}
+
+/// The histogram buffer and its two bind groups, sized to the widget.
+struct Histogram {
+    buffer: wgpu::Buffer,
+    compute_bind_group: wgpu::BindGroup,
+    tonemap_bind_group: wgpu::BindGroup,
+    width: u32,
+    height: u32,
+}
+
+pub struct BuddhabrotRenderer {
+    shader: wgpu::ShaderModule,
+    compute_pipeline_layout: wgpu::PipelineLayout,
+    /// Accumulation pipelines, specialized per fractal kind (the shader's
+    /// `override KIND`, so `advance()` has no per-step kind branches) and
+    /// built lazily on first use.
+    compute_pipelines: HashMap<u32, wgpu::ComputePipeline>,
+    compute_bind_group_layout: wgpu::BindGroupLayout,
+    tonemap_pipeline: wgpu::RenderPipeline,
+    tonemap_bind_group_layout: wgpu::BindGroupLayout,
+    uniform_buffer: wgpu::Buffer,
+    histogram: Option<Histogram>,
+    /// What the current histogram's content was last accumulated for; a
+    /// mismatch clears the histogram and restarts accumulation.
+    last_content: Option<ContentKey>,
+    /// Running sample count since the last reset (mirrors what was written
+    /// into `total_samples`, since the callback doesn't own that state).
+    total_samples: f32,
+    seed: u32,
+}
+
+impl BuddhabrotRenderer {
+    pub fn new(device: &wgpu::Device, target_format: wgpu::TextureFormat) -> Self {
+        let shader = unsafe {
+            device.create_shader_module_trusted(
+                wgpu::ShaderModuleDescriptor {
+                    label: Some("buddhabrot"),
+                    source: wgpu::ShaderSource::Wgsl(
+                        concat!(
+                            include_str!("../shaders/common.wgsl"),
+                            include_str!("../shaders/buddhabrot.wgsl"),
+                        )
+                        .into(),
+                    ),
+                },
+                wgpu::ShaderRuntimeChecks::unchecked(),
+            )
+        };
+
+        let uniform_buffer = device.create_buffer(&wgpu::BufferDescriptor {
+            label: Some("buddhabrot uniforms"),
+            size: std::mem::size_of::<BuddhabrotUniforms>() as u64,
+            usage: wgpu::BufferUsages::UNIFORM | wgpu::BufferUsages::COPY_DST,
+            mapped_at_creation: false,
+        });
+
+        let compute_bind_group_layout =
+            device.create_bind_group_layout(&wgpu::BindGroupLayoutDescriptor {
+                label: Some("buddhabrot compute bind group layout"),
+                entries: &[
+                    wgpu::BindGroupLayoutEntry {
+                        binding: 0,
+                        visibility: wgpu::ShaderStages::COMPUTE,
+                        ty: wgpu::BindingType::Buffer {
+                            ty: wgpu::BufferBindingType::Uniform,
+                            has_dynamic_offset: false,
+                            min_binding_size: None,
+                        },
+                        count: None,
+                    },
+                    wgpu::BindGroupLayoutEntry {
+                        binding: 1,
+                        visibility: wgpu::ShaderStages::COMPUTE,
+                        ty: wgpu::BindingType::Buffer {
+                            ty: wgpu::BufferBindingType::Storage { read_only: false },
+                            has_dynamic_offset: false,
+                            min_binding_size: None,
+                        },
+                        count: None,
+                    },
+                ],
+            });
+        let compute_pipeline_layout =
+            device.create_pipeline_layout(&wgpu::PipelineLayoutDescriptor {
+                label: Some("buddhabrot compute pipeline layout"),
+                bind_group_layouts: &[Some(&compute_bind_group_layout)],
+                immediate_size: 0,
+            });
+
+        let tonemap_bind_group_layout =
+            device.create_bind_group_layout(&wgpu::BindGroupLayoutDescriptor {
+                label: Some("buddhabrot tonemap bind group layout"),
+                entries: &[
+                    wgpu::BindGroupLayoutEntry {
+                        binding: 0,
+                        visibility: wgpu::ShaderStages::FRAGMENT,
+                        ty: wgpu::BindingType::Buffer {
+                            ty: wgpu::BufferBindingType::Uniform,
+                            has_dynamic_offset: false,
+                            min_binding_size: None,
+                        },
+                        count: None,
+                    },
+                    wgpu::BindGroupLayoutEntry {
+                        binding: 2,
+                        visibility: wgpu::ShaderStages::FRAGMENT,
+                        ty: wgpu::BindingType::Buffer {
+                            ty: wgpu::BufferBindingType::Storage { read_only: true },
+                            has_dynamic_offset: false,
+                            min_binding_size: None,
+                        },
+                        count: None,
+                    },
+                ],
+            });
+        let tonemap_pipeline_layout =
+            device.create_pipeline_layout(&wgpu::PipelineLayoutDescriptor {
+                label: Some("buddhabrot tonemap pipeline layout"),
+                bind_group_layouts: &[Some(&tonemap_bind_group_layout)],
+                immediate_size: 0,
+            });
+        let tonemap_pipeline = device.create_render_pipeline(&wgpu::RenderPipelineDescriptor {
+            label: Some("buddhabrot tonemap pipeline"),
+            layout: Some(&tonemap_pipeline_layout),
+            vertex: wgpu::VertexState {
+                module: &shader,
+                entry_point: Some("vs_main"),
+                buffers: &[],
+                compilation_options: Default::default(),
+            },
+            fragment: Some(wgpu::FragmentState {
+                module: &shader,
+                entry_point: Some("fs_tonemap"),
+                targets: &[Some(wgpu::ColorTargetState {
+                    format: target_format,
+                    blend: None,
+                    write_mask: wgpu::ColorWrites::ALL,
+                })],
+                compilation_options: Default::default(),
+            }),
+            primitive: wgpu::PrimitiveState::default(),
+            depth_stencil: None,
+            multisample: wgpu::MultisampleState::default(),
+            multiview_mask: None,
+            cache: None,
+        });
+
+        Self {
+            shader,
+            compute_pipeline_layout,
+            compute_pipelines: HashMap::new(),
+            compute_bind_group_layout,
+            tonemap_pipeline,
+            tonemap_bind_group_layout,
+            uniform_buffer,
+            histogram: None,
+            last_content: None,
+            total_samples: 0.0,
+            seed: 0,
+        }
+    }
+
+    /// The accumulation pipeline for `kind`, built on first use.
+    fn compute_pipeline(&mut self, device: &wgpu::Device, kind: u32) -> &wgpu::ComputePipeline {
+        self.compute_pipelines.entry(kind).or_insert_with(|| {
+            device.create_compute_pipeline(&wgpu::ComputePipelineDescriptor {
+                label: Some("buddhabrot compute pipeline"),
+                layout: Some(&self.compute_pipeline_layout),
+                module: &self.shader,
+                entry_point: Some("cs_main"),
+                compilation_options: wgpu::PipelineCompilationOptions {
+                    constants: &[("KIND", kind as f64)],
+                    ..Default::default()
+                },
+                cache: None,
+            })
+        })
+    }
+
+    /// Ensure the histogram buffer exists at `width`×`height`, recreating (and
+    /// resetting accumulation) on a size change.
+    fn ensure_histogram(&mut self, device: &wgpu::Device, width: u32, height: u32) {
+        if let Some(h) = &self.histogram
+            && h.width == width
+            && h.height == height
+        {
+            return;
+        }
+
+        let plane = (width as u64) * (height as u64);
+        let buffer = device.create_buffer(&wgpu::BufferDescriptor {
+            label: Some("buddhabrot histogram"),
+            size: plane * 3 * std::mem::size_of::<u32>() as u64,
+            usage: wgpu::BufferUsages::STORAGE | wgpu::BufferUsages::COPY_DST,
+            mapped_at_creation: false,
+        });
+
+        let compute_bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
+            label: Some("buddhabrot compute bind group"),
+            layout: &self.compute_bind_group_layout,
+            entries: &[
+                wgpu::BindGroupEntry {
+                    binding: 0,
+                    resource: self.uniform_buffer.as_entire_binding(),
+                },
+                wgpu::BindGroupEntry {
+                    binding: 1,
+                    resource: buffer.as_entire_binding(),
+                },
+            ],
+        });
+        let tonemap_bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
+            label: Some("buddhabrot tonemap bind group"),
+            layout: &self.tonemap_bind_group_layout,
+            entries: &[
+                wgpu::BindGroupEntry {
+                    binding: 0,
+                    resource: self.uniform_buffer.as_entire_binding(),
+                },
+                wgpu::BindGroupEntry {
+                    binding: 2,
+                    resource: buffer.as_entire_binding(),
+                },
+            ],
+        });
+
+        self.histogram = Some(Histogram {
+            buffer,
+            compute_bind_group,
+            tonemap_bind_group,
+            width,
+            height,
+        });
+        // New (zero-initialized) buffer: accumulation starts fresh.
+        self.last_content = None;
+        self.total_samples = 0.0;
+    }
+}
+
+/// Per-frame paint callback. `accumulate` controls whether a new batch of
+/// samples is dispatched this frame (a content change always forces one
+/// dispatch regardless, so a parameter/view change is never left blank).
+pub struct BuddhabrotCallback {
+    pub uniforms: BuddhabrotUniforms,
+    pub accumulate: bool,
+    /// Widget size in physical pixels — the histogram resolution.
+    pub size_px: [u32; 2],
+}
+
+#[cfg(feature = "gui")]
+impl egui_wgpu::CallbackTrait for BuddhabrotCallback {
+    fn prepare(
+        &self,
+        device: &wgpu::Device,
+        queue: &wgpu::Queue,
+        _screen_descriptor: &egui_wgpu::ScreenDescriptor,
+        egui_encoder: &mut wgpu::CommandEncoder,
+        resources: &mut egui_wgpu::CallbackResources,
+    ) -> Vec<wgpu::CommandBuffer> {
+        let Some(renderer) = resources.get_mut::<BuddhabrotRenderer>() else {
+            return Vec::new();
+        };
+
+        let width = self.size_px[0].max(1);
+        let height = self.size_px[1].max(1);
+        renderer.ensure_histogram(device, width, height);
+        let pipeline = renderer
+            .compute_pipeline(device, self.uniforms.kind)
+            .clone();
+
+        let content = ContentKey::from(&self.uniforms);
+        let content_changed = renderer.last_content != Some(content);
+        let should_dispatch = content_changed || self.accumulate;
+
+        if let Some(histogram) = &renderer.histogram {
+            if content_changed {
+                egui_encoder.clear_buffer(&histogram.buffer, 0, None);
+                renderer.total_samples = 0.0;
+                renderer.last_content = Some(content);
+            }
+
+            let mut uniforms = self.uniforms;
+            uniforms.width = width;
+            uniforms.height = height;
+            if should_dispatch {
+                renderer.seed = renderer.seed.wrapping_add(1);
+                renderer.total_samples += SAMPLES_PER_DISPATCH as f32;
+                uniforms.seed = renderer.seed;
+                uniforms.samples_this_dispatch = SAMPLES_PER_DISPATCH;
+            } else {
+                uniforms.samples_this_dispatch = 0;
+            }
+            uniforms.total_samples = renderer.total_samples;
+            queue.write_buffer(&renderer.uniform_buffer, 0, bytemuck::bytes_of(&uniforms));
+
+            if should_dispatch {
+                let mut pass = egui_encoder.begin_compute_pass(&wgpu::ComputePassDescriptor {
+                    label: Some("buddhabrot accumulate pass"),
+                    timestamp_writes: None,
+                });
+                pass.set_pipeline(&pipeline);
+                pass.set_bind_group(0, &histogram.compute_bind_group, &[]);
+                let workgroups = SAMPLES_PER_DISPATCH.div_ceil(WORKGROUP_SIZE);
+                pass.dispatch_workgroups(workgroups, 1, 1);
+            }
+        }
+        Vec::new()
+    }
+
+    fn paint(
+        &self,
+        _info: egui::PaintCallbackInfo,
+        render_pass: &mut wgpu::RenderPass<'static>,
+        resources: &egui_wgpu::CallbackResources,
+    ) {
+        if let Some(renderer) = resources.get::<BuddhabrotRenderer>()
+            && let Some(histogram) = &renderer.histogram
+        {
+            render_pass.set_pipeline(&renderer.tonemap_pipeline);
+            render_pass.set_bind_group(0, &histogram.tonemap_bind_group, &[]);
+            render_pass.draw(0..3, 0..1);
+        }
+    }
+}

src/fractal/kind.rs

@@ -0,0 +1,165 @@
+//! `FractalKind`: the enum selecting which iteration formula is in use, plus
+//! everything that only needs to switch on it (UI label/description/formula
+//! text, share-link tag, default parameter-plane view). The CPU/GPU orbit
+//! math itself lives in `reference.rs` (CPU reference orbit) and
+//! `shaders/mandelbrot.wgsl` (GPU perturbation delta) since both must also
+//! stay in sync with `common.wgsl`'s `KIND_*` constants.
+
+/// The iteration formula. Must be kept in sync with `advance_delta` and the
+/// `KIND_*` constants in the shader.
+#[repr(u8)]
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+pub enum FractalKind {
+    /// `z -> z^2 + c`.
+    Mandelbrot = 0,
+    /// `z -> (|Re z| + i|Im z|)^2 + c`.
+    BurningShip = 1,
+    /// `z -> conj(z)^2 + c` (the Mandelbar).
+    Tricorn = 2,
+    /// `z -> z^power + c` (integer power in [2, 20]).
+    Multibrot = 3,
+    /// `z -> |Re(z^2)| + i·Im(z^2) + c` (abs on the real output of the square).
+    Celtic = 4,
+    /// `z -> (x^2 - y^2) - 2·x·|y|·i + c` (abs on the imaginary input).
+    Perpendicular = 5,
+    /// `z -> |Re(z^2)| - |Im(z^2)|·i + c` (abs on both outputs).
+    Buffalo = 6,
+    /// `z -> z^2 + c + p·z_{n-1}` (two-term recurrence; `p` is `phoenix_p`).
+    Phoenix = 7,
+    /// `z -> lambda·z(1 - z) + c` (logistic map).
+    Lambda = 8,
+    /// `z -> z^power + c`, where `power` is a complex constant (the
+    /// `complex_power` argument), via the principal branch `z^p = exp(p·ln z)`.
+    ComplexMultibrot = 9,
+}
+
+impl FractalKind {
+    /// Every kind, in declaration/discriminant order. Sized arrays keyed by
+    /// `kind as usize` (`JULIA_PRESETS`, `SET_PRESETS`) must have one slot per
+    /// entry here.
+    pub const ALL: [FractalKind; 10] = [
+        FractalKind::Mandelbrot,
+        FractalKind::BurningShip,
+        FractalKind::Tricorn,
+        FractalKind::Multibrot,
+        FractalKind::Celtic,
+        FractalKind::Perpendicular,
+        FractalKind::Buffalo,
+        FractalKind::Phoenix,
+        FractalKind::Lambda,
+        FractalKind::ComplexMultibrot,
+    ];
+
+    pub fn description(&self) -> &'static str {
+        match self {
+            FractalKind::Mandelbrot => {
+                "The Mandelbrot set is the most famous fractal set, obtained with the simplest escape-time formula. This set represents all Julia fractals: each points of the Mandelbrot set is related to a specific Julia fractal."
+            }
+            FractalKind::BurningShip => {
+                "A variation of the famous Mandelbrot set, using absolute values on the real and imaginary part of each iterations."
+            }
+            FractalKind::Tricorn => {
+                "The Tricorn set is obtained using the same formula as the Mandelbrot set, taking the complex conjugate of the previous iteration."
+            }
+            FractalKind::Multibrot => {
+                "Multibrot use the same formula as the Mandelbrot set, with a bigger exposant."
+            }
+            FractalKind::Celtic => "",
+            FractalKind::Perpendicular => "",
+            FractalKind::Buffalo => "",
+            FractalKind::Phoenix => "",
+            FractalKind::Lambda => "",
+            FractalKind::ComplexMultibrot => {
+                "Like Multibrot, but the exponent itself is a complex number instead of a plain integer, via z^p = exp(p·ln z)."
+            }
+        }
+    }
+
+    /// UI label for this kind (combo box / info panel heading).
+    pub fn label(&self) -> &'static str {
+        match self {
+            FractalKind::Mandelbrot => "Mandelbrot",
+            FractalKind::BurningShip => "Burning Ship",
+            FractalKind::Tricorn => "Tricorn",
+            FractalKind::Multibrot => "Multibrot",
+            FractalKind::Celtic => "Celtic",
+            FractalKind::Perpendicular => "Perpendicular",
+            FractalKind::Buffalo => "Buffalo",
+            FractalKind::Phoenix => "Phoenix",
+            FractalKind::Lambda => "Lambda",
+            FractalKind::ComplexMultibrot => "Complex Multibrot",
+        }
+    }
+
+    /// The iteration formula in human-readable notation (mirrors the doc
+    /// comments on the variants above). `power` is only used by Multibrot;
+    /// `complex_power` only by Complex Multibrot.
+    pub fn formula(&self, power: u32, complex_power: (f64, f64)) -> String {
+        match self {
+            FractalKind::Mandelbrot => "z = z² + c".to_string(),
+            FractalKind::BurningShip => "z = (|Re(z)| + i|Im(z)|)² + c".to_string(),
+            FractalKind::Tricorn => "z = conj(z)² + c".to_string(),
+            FractalKind::Multibrot => format!("z = z^{power} + c"),
+            FractalKind::Celtic => "z = |Re(z²)| + i·Im(z²) + c".to_string(),
+            FractalKind::Perpendicular => "z = (x² − y²) − 2x|y|i + c".to_string(),
+            FractalKind::Buffalo => "z = |Re(z²)| − i|Im(z²)| + c".to_string(),
+            FractalKind::Phoenix => "z = z² + c + p·z_prev".to_string(),
+            FractalKind::Lambda => "z = λ·z(1 − z) + c".to_string(),
+            FractalKind::ComplexMultibrot => {
+                format!("z = z^({:.3}{:+.3}i) + c", complex_power.0, complex_power.1)
+            }
+        }
+    }
+
+    /// Short tag used to identify this kind in a share-link fragment.
+    pub fn share_tag(&self) -> &'static str {
+        match self {
+            FractalKind::Mandelbrot => "mandel",
+            FractalKind::BurningShip => "burning",
+            FractalKind::Tricorn => "tricorn",
+            FractalKind::Multibrot => "multi",
+            FractalKind::Celtic => "celtic",
+            FractalKind::Perpendicular => "perp",
+            FractalKind::Buffalo => "buffalo",
+            FractalKind::Phoenix => "phoenix",
+            FractalKind::Lambda => "lambda",
+            FractalKind::ComplexMultibrot => "cmulti",
+        }
+    }
+
+    /// Inverse of `share_tag`; unknown tags fall back to `None` so the caller
+    /// can decide the default (matches historical share-link behavior).
+    pub fn from_share_tag(tag: &str) -> Option<FractalKind> {
+        Some(match tag {
+            "mandel" => FractalKind::Mandelbrot,
+            "burning" => FractalKind::BurningShip,
+            "tricorn" => FractalKind::Tricorn,
+            "multi" => FractalKind::Multibrot,
+            "celtic" => FractalKind::Celtic,
+            "perp" => FractalKind::Perpendicular,
+            "buffalo" => FractalKind::Buffalo,
+            "phoenix" => FractalKind::Phoenix,
+            "lambda" => FractalKind::Lambda,
+            "cmulti" => FractalKind::ComplexMultibrot,
+            _ => return None,
+        })
+    }
+
+    /// Default parameter-plane (Mandelbrot-mode) view for this kind, as
+    /// `(center_re, center_im, half_height)`. The Julia (dynamical) plane
+    /// doesn't vary by kind, so it isn't covered here.
+    pub fn default_set_view(&self) -> (f64, f64, f64) {
+        match self {
+            FractalKind::Mandelbrot => (-0.5, 0.0, 1.25),
+            FractalKind::BurningShip => (-0.5, -0.5, 1.3),
+            FractalKind::Tricorn => (-0.25, 0.0, 1.7),
+            FractalKind::Multibrot => (0.0, 0.0, 1.5),
+            FractalKind::Celtic => (-0.5, 0.0, 1.6),
+            FractalKind::Perpendicular => (-0.5, 0.0, 1.5),
+            FractalKind::Buffalo => (-0.5, 0.5, 1.5),
+            FractalKind::Phoenix => (-0.5, 0.0, 1.5),
+            FractalKind::Lambda => (-0.5, 0.0, 2.4),
+            FractalKind::ComplexMultibrot => (0.0, 0.0, 1.5),
+        }
+    }
+}

src/fractal/mod.rs

@@ -1,13 +1,20 @@
 //! GPU fractal rendering: wgpu pipeline, uniforms, reference orbit, and the
 //! egui paint callback.
 
+pub mod buddhabrot;
+pub mod kind;
 pub mod reference;
 pub mod renderer;
 pub mod share;
 
-pub use reference::{FractalKind, compute_reference, compute_set_reference};
+pub use buddhabrot::{BuddhabrotCallback, BuddhabrotRenderer, BuddhabrotUniforms};
-pub use renderer::{
+pub use kind::FractalKind;
-    ExportRender, FractalCallback, FractalRenderer, MAX_REF_POINTS, Uniforms,
+pub use reference::{RefOrbit, compute_reference, compute_set_reference};
-    encode_png_with_progress,
+#[cfg(not(target_arch = "wasm32"))]
-};
+pub use renderer::PipelineKey;
+#[cfg(target_arch = "wasm32")]
+pub use renderer::encode_png_with_progress;
+pub use renderer::{ExportRender, FractalCallback, FractalRenderer, MAX_REF_POINTS, Uniforms};
+#[cfg(not(target_arch = "wasm32"))]
+pub use renderer::{encode_png, export_to_png_blocking, render_readback_blocking, unpad_rgba};
 pub use share::ShareState;

src/fractal/share.rs

@@ -2,13 +2,14 @@
 //! iterations, Julia constant, coloring) as a compact URL fragment so deep-zoom
 //! locations can be shared or bookmarked.
 //!
-//! Format: `m=m&f=<str>&re=<dec>&im=<dec>&hh=<f64>&it=<u32>&cs=<f32>&co=<f32>` with
+//! Format: `m=m&f=<str>&re=<dec>&im=<dec>&hh=<sci>&it=<u32>&cs=<f32>&co=<f32>` with
 //! `m=j&jr=<f64>&ji=<f64>` added for Julia. `re`/`im` are full-precision decimal
-//! strings.
+//! strings; `hh` is a `Scale` in scientific notation (any exponent).
 
 use std::collections::HashMap;
 
 use crate::fractal::FractalKind;
+use crate::view::Scale;
 
 #[derive(Clone, Debug)]
 pub struct ShareState {
@@ -18,34 +19,43 @@ pub struct ShareState {
     pub power: u32,
     pub center_re: String,
     pub center_im: String,
-    pub half_height: f64,
+    pub half_height: Scale,
     pub iterations: u32,
     pub julia_c: (f64, f64),
+    /// Distortion constant for the Phoenix kind (ignored by others).
+    pub phoenix_p: (f64, f64),
+    /// Distortion constant for the Lambda kind (ignored by others).
+    pub lambda_l: (f64, f64),
+    /// Complex exponent for the Complex Multibrot kind (ignored by others).
+    pub complex_power: (f64, f64),
     pub color_scale: f32,
     pub color_offset: f32,
     /// Palette index (`palette_id` in the shader).
     pub palette: u32,
+    /// Shadow palette index (`shadow_palette_id` in the shader).
+    pub shadow_palette: u32,
 }
 
 impl ShareState {
     pub fn encode(&self) -> String {
         let mut s = String::new();
         s.push_str(if self.julia { "m=j" } else { "m=m" });
-        s.push_str(&format!("&f={}", match self.kind {
+        s.push_str(&format!("&f={}", self.kind.share_tag()));
-            FractalKind::Mandelbrot => "mandel",
-            FractalKind::BurningShip => "burning",
-            FractalKind::Multibrot => "multi",
-            FractalKind::Tricorn => "tricorn",
-        }));
         s.push_str(&format!("&pw={}", self.power));
         s.push_str(&format!(
             "&re={}&im={}&hh={}&it={}",
             self.center_re, self.center_im, self.half_height, self.iterations
         ));
         s.push_str(&format!("&jr={}&ji={}", self.julia_c.0, self.julia_c.1));
+        s.push_str(&format!("&px={}&py={}", self.phoenix_p.0, self.phoenix_p.1));
+        s.push_str(&format!("&lx={}&ly={}", self.lambda_l.0, self.lambda_l.1));
         s.push_str(&format!(
-            "&cs={}&co={}&pal={}",
+            "&cpr={}&cpi={}",
-            self.color_scale, self.color_offset, self.palette
+            self.complex_power.0, self.complex_power.1
+        ));
+        s.push_str(&format!(
+            "&cs={}&co={}&pal={}&spal={}",
+            self.color_scale, self.color_offset, self.palette, self.shadow_palette
         ));
         s
     }
@@ -63,13 +73,7 @@ impl ShareState {
             julia: map.get("m").map(|m| *m == "j").unwrap_or(false),
             kind: map
                 .get("f")
-                .map(|f| match *f {
+                .and_then(|f| FractalKind::from_share_tag(f))
-                    "mandel" => FractalKind::Mandelbrot,
-                    "multi" => FractalKind::Multibrot,
-                    "burning" => FractalKind::BurningShip,
-                    "tricorn" => FractalKind::Tricorn,
-                    _ => FractalKind::Mandelbrot
-                })
                 .unwrap_or(FractalKind::Mandelbrot),
             power: map.get("pw").and_then(|s| s.parse().ok()).unwrap_or(2),
             center_re: (*map.get("re")?).to_string(),
@@ -80,9 +84,22 @@ impl ShareState {
                 map.get("jr").and_then(|s| s.parse().ok()).unwrap_or(-0.8),
                 map.get("ji").and_then(|s| s.parse().ok()).unwrap_or(0.156),
             ),
+            phoenix_p: (
+                map.get("px").and_then(|s| s.parse().ok()).unwrap_or(-0.5),
+                map.get("py").and_then(|s| s.parse().ok()).unwrap_or(0.0),
+            ),
+            lambda_l: (
+                map.get("lx").and_then(|s| s.parse().ok()).unwrap_or(-0.5),
+                map.get("ly").and_then(|s| s.parse().ok()).unwrap_or(0.0),
+            ),
+            complex_power: (
+                map.get("cpr").and_then(|s| s.parse().ok()).unwrap_or(2.0),
+                map.get("cpi").and_then(|s| s.parse().ok()).unwrap_or(0.0),
+            ),
             color_scale: map.get("cs").and_then(|s| s.parse().ok()).unwrap_or(0.02),
             color_offset: map.get("co").and_then(|s| s.parse().ok()).unwrap_or(0.0),
             palette: map.get("pal").and_then(|s| s.parse().ok()).unwrap_or(0),
+            shadow_palette: map.get("spal").and_then(|s| s.parse().ok()).unwrap_or(0),
         })
     }
 }
@@ -95,16 +112,20 @@ mod tests {
     fn round_trip() {
         let s = ShareState {
             julia: true,
-            kind: FractalKind::Multibrot,
+            kind: FractalKind::Phoenix,
             power: 5,
             center_re: "-0.743643887037158704752191506114774".into(),
             center_im: "0.131825904205311970493132056385139".into(),
-            half_height: 1.5e-20,
+            half_height: Scale::from_f64(1.5e-20),
             iterations: 4000,
             julia_c: (-0.123, 0.745),
+            phoenix_p: (-0.5, 0.1),
+            lambda_l: (-0.5, 0.0),
+            complex_power: (2.5, 0.3),
             color_scale: 0.02,
             color_offset: 0.25,
             palette: 3,
+            shadow_palette: 1,
         };
         let d = ShareState::decode(&s.encode()).unwrap();
         assert_eq!(d.julia, s.julia);
@@ -115,7 +136,10 @@ mod tests {
         assert_eq!(d.half_height, s.half_height);
         assert_eq!(d.iterations, s.iterations);
         assert_eq!(d.julia_c, s.julia_c);
+        assert_eq!(d.phoenix_p, s.phoenix_p);
+        assert_eq!(d.complex_power, s.complex_power);
         assert_eq!(d.palette, s.palette);
+        assert_eq!(d.shadow_palette, s.shadow_palette);
     }
 
     #[test]
@@ -123,5 +147,15 @@ mod tests {
         let d = ShareState::decode("#m=m&re=0.0&im=0.0&hh=1.25&it=256").unwrap();
         assert!(!d.julia);
         assert_eq!(d.iterations, 256);
+        assert_eq!(d.half_height, Scale::from_f64(1.25));
+    }
+
+    /// Zooms past f64's range survive a round trip.
+    #[test]
+    fn round_trip_past_f64_range() {
+        let d = ShareState::decode("#m=m&re=0.0&im=0.0&hh=1.5e-1234&it=256").unwrap();
+        assert_eq!(d.half_height, "1.5e-1234".parse().unwrap());
+        let d2 = ShareState::decode(&d.encode()).unwrap();
+        assert_eq!(d2.half_height, d.half_height);
     }
 }

src/headless.rs

@@ -0,0 +1,587 @@
+// Headless PNG rendering: parse the CLI, build the exact same view/state the
+// windowed app would from it, then render straight to a file. No window, no
+// event loop, no worker-thread debounce (nothing to debounce for a one-shot
+// render); it just creates its own wgpu device, computes the reference orbit
+// once, and renders through the same `ExportRender` path the "Export PNG"
+// button uses. `--export-path -` writes to stdout instead: the PNG for a
+// single image, or a raw RGBA8 video stream for an animation (for piping
+// into ffmpeg).
+
+use std::collections::{BTreeMap, HashMap};
+use std::io::{IsTerminal, Write};
+use std::sync::atomic::{AtomicBool, AtomicUsize, Ordering};
+use std::sync::{Mutex, mpsc};
+
+use crate::app::{FractalApp, RefJob, parse_complex_pair, unix_timestamp};
+use crate::cli::Cli;
+use crate::fractal::{
+    ExportRender, FractalKind, FractalRenderer, PipelineKey, ShareState, encode_png,
+    export_to_png_blocking, render_readback_blocking, unpad_rgba,
+};
+use crate::view::{
+    ViewState, big_from_decimal_str, interpolate_f64, interpolate_view, parse_view_spec,
+    precision_for,
+};
+
+/// Cap on the output image dimension (px), to stay within GPU texture limits.
+const MAX_DIM: u32 = 8192 * 16;
+
+/// `--export-path` value meaning "write to stdout".
+const STDOUT_PATH: &str = "-";
+
+/// Refuse to dump binary image data onto a terminal.
+fn check_stdout_piped() -> Result<(), String> {
+    if std::io::stdout().is_terminal() {
+        return Err(
+            "--export-path - writes binary data to stdout; pipe it somewhere \
+                    (e.g. `| ffmpeg ...`)"
+                .into(),
+        );
+    }
+    Ok(())
+}
+
+pub fn run(cli: Cli) -> Result<(), String> {
+    if cli.buddhabrot {
+        return Err("headless mode doesn't support --buddhabrot yet".into());
+    }
+
+    let width = cli.width.clamp(16, MAX_DIM);
+    let height = cli.height.clamp(16, MAX_DIM);
+
+    // These drive the animation path below; grab them before `apply_cli`
+    // consumes `cli` to build the start state.
+    let targets = AnimTargets::from_cli(&cli)?;
+    let export_path = cli.export_path.clone();
+    if export_path.as_deref() == Some(STDOUT_PATH) {
+        check_stdout_piped()?;
+    }
+
+    if targets.shard.is_some() && !targets.any() {
+        return Err("--shard/--shards only apply to animations (give a --to-* target)".into());
+    }
+
+    let mut app = FractalApp::default_state();
+    app.apply_cli(cli);
+    app.set_output_size(width, height);
+
+    if targets.any() {
+        return run_animation(app, targets, width, height, export_path);
+    }
+
+    let export_path = export_path.unwrap_or_else(|| format!("fractal-{}.png", unix_timestamp()));
+
+    eprintln!("computing reference orbit…");
+    app.compute_reference_blocking();
+
+    let (device, queue) = pollster::block_on(request_device())?;
+    let format = wgpu::TextureFormat::Bgra8Unorm;
+    let renderer = FractalRenderer::new(&device, format);
+    let uniforms = app.make_uniforms(width as f64 / height as f64, height as f64);
+    let handles = renderer.export_handles(&device, &uniforms);
+
+    let er = ExportRender::new(
+        &device,
+        &queue,
+        &handles,
+        width,
+        height,
+        uniforms,
+        app.reference_points(),
+        app.lights(),
+    );
+
+    eprintln!("rendering {width}×{height}…");
+    let png = export_to_png_blocking(&device, &queue, &er, |phase, fraction| {
+        eprint!("\r{phase} {:>3.0}%", fraction * 100.0);
+    });
+    eprintln!();
+
+    if export_path == STDOUT_PATH {
+        let mut out = std::io::stdout().lock();
+        out.write_all(&png)
+            .and_then(|()| out.flush())
+            .map_err(|e| format!("writing to stdout failed: {e}"))?;
+        eprintln!("wrote PNG to stdout ({width}×{height})");
+    } else {
+        std::fs::write(&export_path, &png).map_err(|e| format!("save failed: {e}"))?;
+        println!("saved {export_path} ({width}×{height})");
+    }
+    Ok(())
+}
+
+/// The `--to-*` end state of a headless animation, plus its pacing. Each
+/// target is optional; anything left unset stays at its start value.
+struct AnimTargets {
+    to_view: Option<String>,
+    to_share: Option<String>,
+    to_iterations: Option<u32>,
+    to_julia: Option<(f64, f64)>,
+    to_phoenix_p: Option<(f64, f64)>,
+    to_lambda_l: Option<(f64, f64)>,
+    /// Complex Multibrot exponent, per component (either may move alone).
+    to_cpow_re: Option<f64>,
+    to_cpow_im: Option<f64>,
+    to_kind: Option<FractalKind>,
+    /// 3D camera, degrees.
+    to_yaw: Option<f32>,
+    to_pitch: Option<f32>,
+    frames: Option<u32>,
+    fps: f64,
+    duration: Option<f64>,
+    linear: bool,
+    /// `--shard K --shards N`: render only the K-th (1-based) of N parts.
+    shard: Option<(u32, u32)>,
+}
+
+impl AnimTargets {
+    fn from_cli(cli: &Cli) -> Result<Self, String> {
+        let pair = |flag: &str, v: &Option<String>| -> Result<Option<(f64, f64)>, String> {
+            v.as_deref()
+                .map(|s| parse_complex_pair(s).ok_or_else(|| format!("invalid --{flag}: {s}")))
+                .transpose()
+        };
+        let to_cpow = pair("to-complex-power", &cli.to_complex_power)?;
+        let shard = match (cli.shard, cli.shards) {
+            (None, None) | (None, Some(1)) => None,
+            (Some(k), Some(n)) if (1..=n).contains(&k) => Some((k, n)),
+            (Some(k), Some(n)) => {
+                return Err(format!(
+                    "--shard {k} is out of range 1..={n} (--shards {n})"
+                ));
+            }
+            _ => return Err("--shard and --shards must be given together".into()),
+        };
+        Ok(Self {
+            to_view: cli.to_view.clone(),
+            to_share: cli.to_share.clone(),
+            to_iterations: cli.to_iterations,
+            to_julia: pair("to-julia", &cli.to_julia)?,
+            to_phoenix_p: pair("to-phoenix-p", &cli.to_phoenix_p)?,
+            to_lambda_l: pair("to-lambda-l", &cli.to_lambda_l)?,
+            to_cpow_re: cli.to_complex_power_re.or(to_cpow.map(|p| p.0)),
+            to_cpow_im: cli.to_complex_power_im.or(to_cpow.map(|p| p.1)),
+            to_kind: cli.to_kind.map(Into::into),
+            to_yaw: cli.to_yaw,
+            to_pitch: cli.to_pitch,
+            frames: cli.frames,
+            fps: cli.fps,
+            duration: cli.duration,
+            linear: cli.linear,
+            shard,
+        })
+    }
+
+    /// Whether any end state was given, i.e. this is an animation.
+    fn any(&self) -> bool {
+        self.to_view.is_some()
+            || self.to_share.is_some()
+            || self.to_iterations.is_some()
+            || self.to_julia.is_some()
+            || self.to_phoenix_p.is_some()
+            || self.to_lambda_l.is_some()
+            || self.to_cpow_re.is_some()
+            || self.to_cpow_im.is_some()
+            || self.to_kind.is_some()
+            || self.to_yaw.is_some()
+            || self.to_pitch.is_some()
+    }
+}
+
+/// Render a sequence of frames interpolating from the app's current (start)
+/// state to `targets`, for feeding into ffmpeg: the camera, iteration count,
+/// per-kind constants (c, p, λ, complex power) and, through a kind morph,
+/// the iteration formula, and the 3D camera angles. Everything else (colors, ...) stays fixed at
+/// whatever `apply_cli` set up for the start. With `--export-path -`, frames
+/// are streamed in order to stdout as raw RGBA8 (for ffmpeg's `rawvideo`
+/// demuxer) instead of being written as PNGs.
+fn run_animation(
+    mut app: FractalApp,
+    targets: AnimTargets,
+    width: u32,
+    height: u32,
+    export_path: Option<String>,
+) -> Result<(), String> {
+    let fps = targets.fps;
+    let frames = match targets.frames {
+        Some(n) => n,
+        None => {
+            let dur = targets
+                .duration
+                .ok_or("animation needs --frames, or --duration (with --fps)")?;
+            ((fps * dur).round() as u32).max(2)
+        }
+    };
+    if frames < 2 {
+        return Err("animation needs at least 2 frames".into());
+    }
+    // Frames are still timed against the whole animation (`apply_frame` takes
+    // the global index); a shard only picks which of them this run renders.
+    let range = match targets.shard {
+        Some((_, n)) if n > frames => {
+            return Err(format!("--shards {n} is more than the {frames} frames"));
+        }
+        Some((k, n)) => shard_range(frames, k, n),
+        None => 0..frames,
+    };
+    let (first, count) = (range.start, range.len());
+
+    let from = app.view_state().clone();
+    let (to, to_iterations_share) =
+        parse_animation_target(targets.to_view.as_deref(), targets.to_share.as_deref())?
+            .unwrap_or_else(|| (from.clone(), None));
+    let to_iterations = targets.to_iterations.or(to_iterations_share);
+    let from_iterations = app.max_iterations();
+    if to_iterations.is_none() {
+        // Iteration count auto-scales with zoom depth per frame, the same way it
+        // does while zooming interactively — no need to interpolate it by hand.
+        app.set_auto_iterations(true);
+    }
+
+    let from_consts = app.constants();
+    let [c0, p0, l0, cp0] = from_consts;
+    let to_consts = [
+        targets.to_julia.unwrap_or(c0),
+        targets.to_phoenix_p.unwrap_or(p0),
+        targets.to_lambda_l.unwrap_or(l0),
+        (
+            targets.to_cpow_re.unwrap_or(cp0.0),
+            targets.to_cpow_im.unwrap_or(cp0.1),
+        ),
+    ];
+    let from_kind = app.kind();
+    let to_kind = targets.to_kind.unwrap_or(from_kind);
+    let (yaw0, pitch0) = app.camera_angles();
+    let yaw1 = targets.to_yaw.map_or(yaw0, f32::to_radians);
+    let pitch1 = targets.to_pitch.map_or(pitch0, f32::to_radians);
+
+    let stream = export_path.as_deref() == Some(STDOUT_PATH);
+    let out_dir = export_path.unwrap_or_else(|| format!("frames-{}", unix_timestamp()));
+    if stream {
+        eprintln!(
+            "streaming raw video to stdout; ffmpeg input: \
+             -f rawvideo -pix_fmt rgba -s {width}x{height} -r {fps} -i -"
+        );
+    } else {
+        std::fs::create_dir_all(&out_dir)
+            .map_err(|e| format!("failed to create {out_dir}: {e}"))?;
+    }
+
+    // Everything about frame `i` is a pure function of its `t`, so the app can
+    // be put into any frame's state at any time, in any order.
+    let apply_frame = |app: &mut FractalApp, i: u32| {
+        let raw_t = i as f64 / (frames - 1) as f64;
+        let t = if targets.linear {
+            raw_t
+        } else {
+            smoothstep(raw_t)
+        };
+        if let Some(to) = to_iterations {
+            app.set_max_iterations(
+                interpolate_f64(from_iterations as f64, to as f64, t).round() as u32,
+            );
+        }
+        app.set_view(interpolate_view(&from, &to, t));
+        app.set_constants(std::array::from_fn(|k| {
+            (
+                interpolate_f64(from_consts[k].0, to_consts[k].0, t),
+                interpolate_f64(from_consts[k].1, to_consts[k].1, t),
+            )
+        }));
+        app.set_kind_morph(from_kind, to_kind, t);
+        app.set_camera_angles(
+            interpolate_f64(yaw0 as f64, yaw1 as f64, t) as f32,
+            interpolate_f64(pitch0 as f64, pitch1 as f64, t) as f32,
+        );
+    };
+
+    // Snapshot every frame's reference-orbit job up front (cheap: just the
+    // parameters), so the orbits themselves can be computed in parallel.
+    // `jobs[j]` is global frame `first + j`; the pipeline below works in
+    // local indices `j`, so the stdout writer's ordering is per shard.
+    let jobs: Vec<RefJob> = range
+        .clone()
+        .map(|i| {
+            apply_frame(&mut app, i);
+            app.reference_job()
+        })
+        .collect();
+
+    let (device, queue) = pollster::block_on(request_device())?;
+    let format = wgpu::TextureFormat::Bgra8Unorm;
+    let renderer = FractalRenderer::new(&device, format);
+    let aspect = width as f64 / height as f64;
+
+    // Three-stage pipeline, connected by bounded channels (which also cap
+    // memory): `threads` workers compute reference orbits (CPU, the expensive
+    // part at deep zoom) → this thread renders each frame on the GPU → `threads`
+    // workers PNG-encode and write frames. Frames flow through out of order
+    // (at most ~`threads` apart); each is written under its own index.
+    //
+    // When streaming, the last stage instead unpads frames to raw RGBA and a
+    // single writer thread puts them back in order before writing to stdout.
+    // Its reorder buffer can't apply backpressure (blocking it while waiting
+    // for frame `k` could stall the pipeline before `k` gets through), so the
+    // orbit workers bound it instead: they don't start a frame more than
+    // `window` ahead of the last one written.
+    let threads = std::thread::available_parallelism().map_or(4, |n| n.get());
+    let window = threads * 4;
+    let next_job = AtomicUsize::new(0);
+    let saved = AtomicUsize::new(0);
+    let failed = AtomicBool::new(false);
+    let error: Mutex<Option<String>> = Mutex::new(None);
+    let fail = |e: String| {
+        failed.store(true, Ordering::Relaxed);
+        error.lock().unwrap().get_or_insert(e);
+    };
+
+    if let Some((k, n)) = targets.shard {
+        eprintln!(
+            "shard {k}/{n}: frames {}–{} of {frames}",
+            range.start + 1,
+            range.end
+        );
+    }
+    eprintln!("rendering {count} frames ({width}×{height}) on {threads} threads…");
+    let (png_tx, png_rx) = mpsc::sync_channel::<(usize, Vec<u8>, u32, bool)>(threads * 2);
+    let png_rx = Mutex::new(png_rx);
+    let (raw_tx, raw_rx) = mpsc::sync_channel::<(usize, Vec<u8>)>(threads * 2);
+    std::thread::scope(|scope| {
+        let (ref_tx, ref_rx) = mpsc::sync_channel::<(usize, crate::fractal::RefOrbit)>(threads * 2);
+        for _ in 0..threads {
+            let ref_tx = ref_tx.clone();
+            let (jobs, next_job, saved, failed) = (&jobs, &next_job, &saved, &failed);
+            scope.spawn(move || {
+                loop {
+                    let i = next_job.fetch_add(1, Ordering::Relaxed);
+                    if i >= jobs.len() || failed.load(Ordering::Relaxed) {
+                        break;
+                    }
+                    while stream
+                        && i >= saved.load(Ordering::Relaxed) + window
+                        && !failed.load(Ordering::Relaxed)
+                    {
+                        std::thread::sleep(std::time::Duration::from_millis(2));
+                    }
+                    if ref_tx.send((i, jobs[i].compute())).is_err() {
+                        break;
+                    }
+                }
+            });
+        }
+        drop(ref_tx);
+
+        if stream {
+            let (saved, fail) = (&saved, &fail);
+            scope.spawn(move || {
+                let mut out = std::io::stdout().lock();
+                let mut pending = BTreeMap::new();
+                let mut next = 0;
+                for (i, raw) in raw_rx.iter() {
+                    pending.insert(i, raw);
+                    while let Some(raw) = pending.remove(&next) {
+                        if let Err(e) = out.write_all(&raw) {
+                            fail(format!("writing to stdout failed: {e}"));
+                            return;
+                        }
+                        next += 1;
+                        saved.store(next, Ordering::Relaxed);
+                        eprint!("\r[{next:>4}/{count}] streamed");
+                    }
+                }
+                if let Err(e) = out.flush() {
+                    fail(format!("writing to stdout failed: {e}"));
+                }
+            });
+        } else {
+            drop(raw_rx);
+        }
+
+        for _ in 0..threads {
+            let raw_tx = raw_tx.clone();
+            let (png_rx, out_dir, saved, failed, fail) =
+                (&png_rx, &out_dir, &saved, &failed, &fail);
+            scope.spawn(move || {
+                loop {
+                    // Hold the lock only for the receive, not the encode.
+                    let Ok((i, padded, bpr, swap_rb)) = png_rx.lock().unwrap().recv() else {
+                        break;
+                    };
+                    // After a failure, keep draining (without work) until the
+                    // GPU stage hangs up, so it can't block on a full channel.
+                    if failed.load(Ordering::Relaxed) {
+                        continue;
+                    }
+                    if stream {
+                        let raw = unpad_rgba(&padded, width, height, bpr, swap_rb);
+                        // Only fails once the writer has failed and hung up.
+                        let _ = raw_tx.send((i, raw));
+                        continue;
+                    }
+                    let png =
+                        encode_png(&padded, width, height, bpr, swap_rb, png::Compression::Fast);
+                    let path = format!("{out_dir}/frame-{:05}.png", first as usize + i + 1);
+                    if let Err(e) = std::fs::write(&path, &png) {
+                        fail(format!("save failed: {e}"));
+                        continue;
+                    }
+                    let done = saved.fetch_add(1, Ordering::Relaxed) + 1;
+                    eprint!("\r[{done:>4}/{count}] saved");
+                }
+            });
+        }
+
+        // GPU stage, on this thread (it owns the app and the device). The
+        // shader specialization (kind, Julia, DE, morph) can change between
+        // frames during a kind morph; build each pipeline once.
+        let mut pipelines = HashMap::new();
+        for (i, points) in ref_rx.iter() {
+            if failed.load(Ordering::Relaxed) {
+                break;
+            }
+            apply_frame(&mut app, first + i as u32);
+            app.finish_reference(jobs[i].clone(), points);
+
+            let uniforms = app.make_uniforms(aspect, height as f64);
+            let handles = pipelines
+                .entry(PipelineKey::from_uniforms(&uniforms))
+                .or_insert_with(|| renderer.export_handles(&device, &uniforms));
+            let er = ExportRender::new(
+                &device,
+                &queue,
+                handles,
+                width,
+                height,
+                uniforms,
+                app.reference_points(),
+                app.lights(),
+            );
+            let padded = render_readback_blocking(&device, &queue, &er);
+            if png_tx.send((i, padded, er.padded_bpr, er.swap_rb)).is_err() {
+                break;
+            }
+        }
+        // Dropping the channel ends lets the workers drain and exit.
+        drop(raw_tx);
+        drop(png_tx);
+        drop(ref_rx);
+    });
+    eprintln!();
+
+    if let Some(e) = error.into_inner().unwrap() {
+        return Err(e);
+    }
+    let saved = saved.into_inner();
+    if saved != count {
+        return Err(format!("only {saved} of {count} frames were rendered"));
+    }
+
+    if stream {
+        eprintln!("streamed {count} frames ({width}×{height})");
+        return Ok(());
+    }
+    println!("saved {count} frames to {out_dir}/ ({width}×{height})");
+    if targets.shard.is_some() {
+        println!(
+            "tip: once every shard is rendered into {out_dir}/, they form the full sequence; \
+             this shard alone: ffmpeg -framerate {fps} -start_number {} -i {out_dir}/frame-%05d.png \
+             -frames:v {count} -c:v libx264 -pix_fmt yuv420p out.mp4",
+            range.start + 1
+        );
+    } else {
+        println!(
+            "tip: ffmpeg -framerate {fps} -i {out_dir}/frame-%05d.png -c:v libx264 -pix_fmt yuv420p out.mp4"
+        );
+    }
+    Ok(())
+}
+
+/// Parse `--to-view`/`--to-share` (at most one is used) into the end view
+/// of an animation, or `None` if neither is set (the camera stays put). Only position/zoom/iterations are pulled from a
+/// share fragment — the rest of its state (kind, colors, ...) is ignored, so
+/// pasting a link from the app doesn't unexpectedly change the fractal kind
+/// mid-animation.
+fn parse_animation_target(
+    to_view: Option<&str>,
+    to_share: Option<&str>,
+) -> Result<Option<(ViewState, Option<u32>)>, String> {
+    if let Some(spec) = to_view {
+        return parse_view_spec(spec)
+            .map(Some)
+            .ok_or_else(|| format!("invalid --to-view spec: {spec}"));
+    }
+    let Some(frag) = to_share else {
+        return Ok(None);
+    };
+    let state =
+        ShareState::decode(frag).ok_or_else(|| format!("invalid --to-share fragment: {frag}"))?;
+    let bits = precision_for(state.half_height);
+    let re =
+        big_from_decimal_str(&state.center_re, bits).ok_or("invalid --to-share center (re)")?;
+    let im =
+        big_from_decimal_str(&state.center_im, bits).ok_or("invalid --to-share center (im)")?;
+    Ok(Some((
+        ViewState::with_center(re, im, state.half_height),
+        Some(state.iterations),
+    )))
+}
+
+/// Global frame indices of shard `shard` (1-based) out of `shards` equal
+/// parts of a `frames`-frame animation. Consecutive shards tile `0..frames`
+/// with no gap or overlap.
+fn shard_range(frames: u32, shard: u32, shards: u32) -> std::ops::Range<u32> {
+    let bound = |k: u32| (k as u64 * frames as u64 / shards as u64) as u32;
+    bound(shard - 1)..bound(shard)
+}
+
+/// Ease-in/ease-out pacing: slow at both ends, fast through the middle.
+fn smoothstep(t: f64) -> f64 {
+    t * t * (3.0 - 2.0 * t)
+}
+
+/// Set up a wgpu device with no surface/window attached, matching the limits
+/// `main::wgpu_options` requests for the windowed app (the fractal fragment
+/// shader needs storage buffers, which downlevel/WebGL-style limits disallow).
+async fn request_device() -> Result<(wgpu::Device, wgpu::Queue), String> {
+    let instance = wgpu::Instance::default();
+    let adapter = instance
+        .request_adapter(&wgpu::RequestAdapterOptions::default())
+        .await
+        .map_err(|e| format!("no compatible GPU adapter: {e}"))?;
+    adapter
+        .request_device(&wgpu::DeviceDescriptor {
+            label: Some("headless fractal device"),
+            required_features: wgpu::Features::empty(),
+            required_limits: adapter.limits(),
+            ..Default::default()
+        })
+        .await
+        .map_err(|e| format!("failed to create device: {e}"))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::shard_range;
+
+    #[test]
+    fn shards_tile_all_frames() {
+        for frames in [2, 3, 10, 97, 1000, u32::MAX] {
+            for shards in [1, 2, 3, 7, 10] {
+                if shards > frames {
+                    continue;
+                }
+                let mut next = 0;
+                for k in 1..=shards {
+                    let r = shard_range(frames, k, shards);
+                    assert_eq!(
+                        r.start, next,
+                        "gap/overlap at shard {k}/{shards} of {frames}"
+                    );
+                    assert!(!r.is_empty(), "empty shard {k}/{shards} of {frames}");
+                    next = r.end;
+                }
+                assert_eq!(next, frames);
+            }
+        }
+    }
+}

src/lights.rs

@@ -0,0 +1,97 @@
+use std::f32::consts::PI;
+
+use bytemuck::{Pod, Zeroable};
+use ecolor::Color32;
+#[cfg(feature = "gui")]
+use egui::Ui;
+
+/// Maximum number of simultaneous lights.
+pub const MAX_LIGHT_COUNT: usize = 16;
+
+#[derive(Clone, Copy, PartialEq, Zeroable, Pod)]
+#[repr(C)]
+pub struct Light {
+    pub azimuth: f32,
+    pub altitude: f32,
+    pub color: Color32,
+    pub _pad: u32,
+}
+
+impl Default for Light {
+    fn default() -> Self {
+        Self {
+            azimuth: PI / 4.,
+            altitude: PI / 4.,
+            color: Color32::WHITE,
+            _pad: 0,
+        }
+    }
+}
+
+impl Light {
+    #[cfg(feature = "gui")]
+    pub fn widget(&mut self, ui: &mut Ui) -> bool {
+        let formater = |v, _| format!("{}°", ((v * 180. / std::f64::consts::PI) as u32));
+        let parser = |s: &str| {
+            s.parse::<u32>()
+                .ok()
+                .map(|x| x as f64 * std::f64::consts::PI / 180.)
+        };
+        ui.horizontal(|ui| {
+            let del = ui.button("-").clicked();
+            ui.label("color:");
+            ui.color_edit_button_srgba(&mut self.color);
+            ui.label("θ:");
+            ui.add(
+                egui::DragValue::new(&mut self.azimuth)
+                    .range(0.0..=PI * 2.)
+                    .custom_formatter(formater)
+                    .custom_parser(parser)
+                    .speed(0.02),
+            );
+            ui.label("φ:");
+            ui.add(
+                egui::DragValue::new(&mut self.altitude)
+                    .range(0.0..=PI / 2.)
+                    .custom_formatter(formater)
+                    .custom_parser(parser)
+                    .speed(0.02),
+            );
+
+            del
+        })
+        .inner
+    }
+}
+
+/// GPU-side light, matching WGSL `Light` in `iterate_uniforms.wgsl`: the unit
+/// direction toward the light (precomputed from azimuth/altitude so the
+/// shader does no per-pixel trig) plus the packed RGBA colour, whose alpha is
+/// the intensity. 16 bytes, so `array<Light, 16>` has a uniform-legal stride.
+#[derive(Clone, Copy, PartialEq, Zeroable, Pod, Default)]
+#[repr(C)]
+pub struct GpuLight {
+    pub dir: [f32; 3],
+    pub color: Color32,
+}
+
+/// The light buffer's contents: the UI lights with a non-zero colour (the
+/// only ones that contribute, and the ones the filmic white point counts),
+/// packed to the front, plus how many there are (`Uniforms::light_count`).
+pub fn gpu_lights(lights: &[Light]) -> ([GpuLight; MAX_LIGHT_COUNT], u32) {
+    let mut out = [GpuLight::default(); MAX_LIGHT_COUNT];
+    let mut n = 0;
+    for l in lights.iter().filter(|l| l.color != Color32::TRANSPARENT) {
+        if n == MAX_LIGHT_COUNT {
+            break;
+        }
+        let (sa, ca) = l.altitude.sin_cos();
+        let (sz, cz) = l.azimuth.sin_cos();
+        out[n] = GpuLight {
+            dir: [cz * ca, sz * ca, sa],
+            color: l.color,
+        };
+        n += 1;
+    }
+    (out, n as u32)
+}

src/main.rs

@@ -1,3 +1,9 @@
+// Without these, rust fails to infer Send/Sync trait impls
+// Probably caused by the new trait solver
+#![recursion_limit = "256"]
+// Without the `gui` feature, UI-only state and helpers go unused.
+#![cfg_attr(not(feature = "gui"), allow(dead_code, unused_imports))]
+
 // Fractal Explorer — Rust + wgpu + egui + WGSL deep-zoom Mandelbrot.
 //
 // A single binary drives both native and web (WASM/WebGPU) builds; the two
@@ -5,14 +11,30 @@
 // and calls the wasm `main`, which boots eframe onto the page's <canvas>.
 
 mod app;
+mod bignum;
+mod camera;
 mod fractal;
+mod lights;
 mod view;
 
+#[cfg(not(target_arch = "wasm32"))]
+mod cli;
+#[cfg(not(target_arch = "wasm32"))]
+mod headless;
 #[cfg(not(target_arch = "wasm32"))]
 mod worker;
 
+#[cfg(all(target_arch = "wasm32", not(feature = "gui")))]
+compile_error!("the web build needs the `gui` feature");
+
+#[cfg(feature = "gui")]
 use app::FractalApp;
 
+#[cfg(all(feature = "gui", not(target_arch = "wasm32")))]
+type MainResult = eframe::Result;
+#[cfg(all(not(feature = "gui"), not(target_arch = "wasm32")))]
+type MainResult = Result<(), String>;
+
 /// wgpu configuration for eframe. The fractal fragment shader reads the
 /// reference orbit from a **storage buffer**, so the device must allow storage
 /// buffers in the fragment stage. eframe's default requests WebGL2-downlevel
@@ -20,18 +42,18 @@ use app::FractalApp;
 ///   * request the adapter's real limits (which include storage buffers), and
 ///   * force the WebGPU backend on the web (WebGL2 can't do storage buffers at
 ///     all) — failing cleanly on browsers without WebGPU, per the design.
+#[cfg(feature = "gui")]
 fn wgpu_options() -> eframe::egui_wgpu::WgpuConfiguration {
     use eframe::egui_wgpu::{WgpuSetup, wgpu};
 
     let mut options = eframe::egui_wgpu::WgpuConfiguration::default();
     if let WgpuSetup::CreateNew(setup) = &mut options.wgpu_setup {
-        setup.device_descriptor = std::sync::Arc::new(|adapter: &wgpu::Adapter| {
+        setup.device_descriptor =
-            wgpu::DeviceDescriptor {
+            std::sync::Arc::new(|adapter: &wgpu::Adapter| wgpu::DeviceDescriptor {
                 label: Some("fractal wgpu device"),
                 required_features: wgpu::Features::empty(),
                 required_limits: adapter.limits(),
                 ..Default::default()
-            }
             });
         #[cfg(target_arch = "wasm32")]
         {
@@ -42,12 +64,32 @@ fn wgpu_options() -> eframe::egui_wgpu::WgpuConfiguration {
 }
 
 #[cfg(not(target_arch = "wasm32"))]
-fn main() -> eframe::Result {
+fn main() -> MainResult {
+    use clap::Parser as _;
+
     env_logger::builder()
         .filter_level(log::LevelFilter::Info)
         .parse_default_env()
         .init();
 
+    let cli = cli::Cli::parse();
+    if cli.headless {
+        return match headless::run(cli) {
+            Ok(()) => Ok(()),
+            Err(e) => {
+                eprintln!("error: {e}");
+                std::process::exit(1);
+            }
+        };
+    }
+
+    #[cfg(not(feature = "gui"))]
+    {
+        eprintln!("error: built without the \"gui\" feature; only --headless is supported");
+        std::process::exit(1);
+    }
+
+    #[cfg(feature = "gui")]
     let native_options = eframe::NativeOptions {
         renderer: eframe::Renderer::Wgpu,
         wgpu_options: wgpu_options(),
@@ -58,6 +100,7 @@ fn main() -> eframe::Result {
         ..Default::default()
     };
 
+    #[cfg(feature = "gui")]
     eframe::run_native(
         "Fractal Explorer",
         native_options,
@@ -101,9 +144,7 @@ fn main() {
             match result {
                 Ok(_) => loading.remove(),
                 Err(e) => {
-                    loading.set_inner_html(
+                    loading.set_inner_html(&format!("<p>The app has crashed.</br>{e:?}</p>"));
-                        "<p>The app has crashed. See the developer console for details.</p>",
-                    );
                     log::error!("failed to start eframe: {e:?}");
                 }
             }

src/shaders/blit.wgsl

@@ -13,12 +13,7 @@ struct VsOut {
 
 @vertex
 fn vs_main(@builtin(vertex_index) idx: u32) -> VsOut {
-    var verts = array<vec2<f32>, 3>(
+    let p = fullscreen_triangle_pos(idx);
-        vec2<f32>(-1.0, -1.0),
-        vec2<f32>(3.0, -1.0),
-        vec2<f32>(-1.0, 3.0),
-    );
-    let p = verts[idx];
     var out: VsOut;
     out.pos = vec4<f32>(p, 0.0, 1.0);
     // Map NDC to texture UV. v is flipped so the cache's top row (rendered at

src/shaders/buddhabrot.wgsl

@@ -0,0 +1,289 @@
+// Buddhabrot / Nebulabrot rendering: a Monte-Carlo density histogram of
+// escaping orbits, accumulated progressively across frames by a compute pass,
+// then tone-mapped to colour by a fragment pass every frame.
+//
+// This does NOT use the deep-zoom perturbation/reference-orbit machinery in
+// mandelbrot.wgsl: Buddhabrot's structure is a global Monte-Carlo property of
+// the whole basin (a random sample's orbit scatters across the *whole* image,
+// not just its own pixel), so the "gather" per-pixel model doesn't apply, and
+// deep zoom isn't meaningful for it the way it is for the escape-time set.
+// Samples are iterated directly in f32 from the current view's bounds.
+//
+// Sampling convention: for KIND_LAMBDA the formula z -> l*z*(1-z) has no `c`
+// term at all (l is a fixed distortion constant, not a per-sample parameter),
+// so the randomly sampled point instead seeds z0 (a "Julia-Buddhabrot" over
+// z0 with l fixed). Every other kind samples c with z0 = 0, matching its
+// ordinary parameter plane.
+//
+// A sample's orbit is only plotted if it escapes within b_cap iterations (the
+// classic Buddhabrot rule: only escaping orbits are drawn). Its points are
+// then splat into up to three histogram channels by cap (r_cap <= g_cap <=
+// b_cap): fast-escaping (common) orbits light all three channels (bright),
+// slow-escaping (rare) orbits only light the b_cap channel — the classic
+// Nebulabrot false-colour split.
+//
+// Two-pass iteration avoids needing a per-thread orbit buffer sized to
+// max_iter: the first pass just finds the escape iteration (if any); the
+// second replays the same orbit from scratch, splatting each point.
+
+struct Uniforms {
+    center: vec2<f32>,
+    half_height: f32,
+    aspect: f32,
+    phoenix_p: vec2<f32>,
+    lambda_l: vec2<f32>,
+    bailout_sq: f32,
+    kind: u32,
+    power: u32,
+    r_cap: u32,
+    g_cap: u32,
+    b_cap: u32,
+    seed: u32,
+    samples_this_dispatch: u32,
+    exposure: f32,
+    width: u32,
+    height: u32,
+    total_samples: f32,
+    // Tonemap colour style: 0 = classic (R/G/B = raw caps), 1 = nebula
+    // (yellow core, blue halo), 2 = grayscale.
+    palette: u32,
+    // Padding so `complex_power` (a vec2, 8-byte aligned) starts on an
+    // 8-byte boundary. NOT vec3<u32> — that type aligns to 16 bytes in WGSL
+    // (unlike Rust's `[u32; 3]`, which aligns to 4), which silently added 32
+    // bytes instead of 16 and mismatched the Rust struct's size (a wgpu
+    // validation error at dispatch time: "size 96 where the shader expects
+    // 112").
+    _pad0: u32,
+    // Complex exponent for the Complex Multibrot kind; unused by other kinds.
+    complex_power: vec2<f32>,
+};
+
+// Fractal kind, as a pipeline-overridable constant (set per compute pipeline
+// from `u.kind`, see `BuddhabrotRenderer::compute_pipeline`): every kind
+// branch in the iteration loop folds away at pipeline creation. Read this,
+// never `u.kind`.
+override KIND: u32 = 0u;
+
+const PALETTE_NEBULA: u32 = 0u;
+const PALETTE_YELLOW: u32 = 1u;
+const PALETTE_GRAYSCALE: u32 = 2u;
+
+@group(0) @binding(0) var<uniform> u: Uniforms;
+// Compute pass: read-write atomic histogram (3 planes of width*height, R/G/B).
+@group(0) @binding(1) var<storage, read_write> histogram: array<atomic<u32>>;
+// Tonemap pass: read-only plain view of the same buffer.
+@group(0) @binding(2) var<storage, read> tm_histogram: array<u32>;
+
+// --- RNG: a small, fast integer hash (WGSL has no native RNG). ---
+fn hash_u32(x: u32) -> u32 {
+    var h = x;
+    h = h ^ (h >> 16u);
+    h = h * 0x7feb352du;
+    h = h ^ (h >> 15u);
+    h = h * 0x846ca68bu;
+    h = h ^ (h >> 16u);
+    return h;
+}
+fn rand01(seed: u32) -> f32 {
+    return f32(hash_u32(seed)) * (1.0 / 4294967295.0);
+}
+
+fn complex_pow(z: vec2<f32>, p: u32) -> vec2<f32> {
+    var r = vec2<f32>(1.0, 0.0);
+    for (var i: u32 = 0u; i < p; i = i + 1u) {
+        r = cmul(r, z);
+    }
+    return r;
+}
+
+// One iteration step z_n -> z_{n+1} for the current kind. `zp` is the
+// previous iterate (z_{n-1}), used only by the Phoenix two-term recurrence.
+// Must match `FractalKind` in reference.rs (the direct, non-perturbative form
+// of the same formulas).
+fn advance(z: vec2<f32>, zp: vec2<f32>, c: vec2<f32>) -> vec2<f32> {
+    if KIND == KIND_BURNING_SHIP {
+        return vec2<f32>(z.x * z.x - z.y * z.y, 2.0 * abs(z.x * z.y)) + c;
+    } else if KIND == KIND_TRICORN {
+        return vec2<f32>(z.x * z.x - z.y * z.y, -2.0 * z.x * z.y) + c;
+    } else if KIND == KIND_MULTIBROT {
+        return complex_pow(z, clamp(u.power, 2u, MULTIBROT_MAX_POWER)) + c;
+    } else if KIND == KIND_CELTIC {
+        return vec2<f32>(abs(z.x * z.x - z.y * z.y), 2.0 * z.x * z.y) + c;
+    } else if KIND == KIND_PERPENDICULAR {
+        return vec2<f32>(z.x * z.x - z.y * z.y, -2.0 * z.x * abs(z.y)) + c;
+    } else if KIND == KIND_BUFFALO {
+        return vec2<f32>(abs(z.x * z.x - z.y * z.y), -abs(2.0 * z.x * z.y)) + c;
+    } else if KIND == KIND_PHOENIX {
+        let sq = vec2<f32>(z.x * z.x - z.y * z.y, 2.0 * z.x * z.y);
+        return sq + c + cmul(u.phoenix_p, zp);
+    } else if KIND == KIND_LAMBDA {
+        // l * z * (1 - z); c is unused (see file doc comment above).
+        return cmul(u.lambda_l, cmul(z, vec2<f32>(1.0 - z.x, -z.y)));
+    } else if KIND == KIND_COMPLEX_MULTIBROT {
+        return cpow(z, u.complex_power) + c;
+    }
+    return vec2<f32>(z.x * z.x - z.y * z.y, 2.0 * z.x * z.y) + c; // Mandelbrot
+}
+
+// Map a complex-plane point to a flat pixel index, or -1 if outside the
+// current viewport (the sampling region and the display region are the same).
+//
+// This must be the exact inverse of how `view.rs::pan_pixels`/`zoom_at_pixel`
+// relate screen pixels to world points (those are the confirmed-correct,
+// user-tested ground truth — NOT the shader-comment-derived convention tried
+// here previously, which was wrong: dragging/zooming treat +y screen exactly
+// like +x, no flip, so screen-down means im *increasing*, not decreasing).
+fn pixel_index(p: vec2<f32>) -> i32 {
+    let half_w = u.half_height * u.aspect;
+    let uu = (p.x - u.center.x) / half_w * 0.5 + 0.5;
+    let vv = 0.5 + (p.y - u.center.y) / u.half_height * 0.5;
+    if uu < 0.0 || uu >= 1.0 || vv < 0.0 || vv >= 1.0 {
+        return -1;
+    }
+    let px = i32(uu * f32(u.width));
+    let py = i32(vv * f32(u.height));
+    return py * i32(u.width) + px;
+}
+
+// Splat one visited orbit point into the R/G/B histogram planes it qualifies
+// for by the orbit's total escape iteration `n` (nested caps: a fast escape
+// lights all three; only a slow, rare one lights just the blue plane).
+fn splat(p: vec2<f32>, n: u32) {
+    let idx = pixel_index(p);
+    if idx < 0 {
+        return;
+    }
+    let plane = i32(u.width) * i32(u.height);
+    if n <= u.b_cap {
+        atomicAdd(&histogram[idx + 2 * plane], 1u);
+    }
+    if n <= u.g_cap {
+        atomicAdd(&histogram[idx + plane], 1u);
+    }
+    if n <= u.r_cap {
+        atomicAdd(&histogram[idx], 1u);
+    }
+}
+
+@compute @workgroup_size(64)
+fn cs_main(@builtin(global_invocation_id) gid: vec3<u32>) {
+    if gid.x >= u.samples_this_dispatch {
+        return;
+    }
+
+    let base = hash_u32(gid.x ^ (u.seed * 0x9e3779b9u));
+    let rx = rand01(base);
+    let ry = rand01(hash_u32(base ^ 0x68bc21ebu));
+    let half_w = u.half_height * u.aspect;
+    let sample = vec2<f32>(
+        u.center.x + (rx * 2.0 - 1.0) * half_w,
+        u.center.y + (ry * 2.0 - 1.0) * u.half_height,
+    );
+
+    var c = sample;
+    var z0 = vec2<f32>(0.0, 0.0);
+    if KIND == KIND_LAMBDA {
+        c = vec2<f32>(0.0, 0.0); // unused by the Lambda step
+        z0 = sample;
+    }
+
+    // First pass: just find the escape iteration (if any).
+    var zp = vec2<f32>(0.0, 0.0);
+    var z = z0;
+    var n: u32 = 0u;
+    var escaped = false;
+    loop {
+        if dot(z, z) > u.bailout_sq {
+            escaped = true;
+            break;
+        }
+        if n >= u.b_cap {
+            break;
+        }
+        let next = advance(z, zp, c);
+        zp = z;
+        z = next;
+        n = n + 1u;
+    }
+    if !escaped || n == 0u {
+        return;
+    }
+
+    // Second pass: replay the same orbit, splatting each visited point.
+    // z0 itself is not splat: it's the same fixed point (0,0), or the sample
+    // itself for Lambda, for every orbit — plotting it would just spike the
+    // origin instead of showing the orbit's actual shape.
+    zp = vec2<f32>(0.0, 0.0);
+    z = z0;
+    for (var i: u32 = 0u; i < n; i = i + 1u) {
+        let next = advance(z, zp, c);
+        zp = z;
+        z = next;
+        splat(z, n);
+    }
+}
+
+// --- Tonemap: histogram counts -> colour, drawn as a fullscreen triangle. ---
+
+@vertex
+fn vs_main(@builtin(vertex_index) idx: u32) -> @builtin(position) vec4<f32> {
+    return vec4<f32>(fullscreen_triangle_pos(idx), 0.0, 1.0);
+}
+
+@fragment
+fn fs_tonemap(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
+    let x = i32(pos.x);
+    let y = i32(pos.y);
+    if x < 0 || y < 0 || x >= i32(u.width) || y >= i32(u.height) {
+        return vec4<f32>(0.0, 0.0, 0.0, 1.0);
+    }
+    let idx = y * i32(u.width) + x;
+    let plane = i32(u.width) * i32(u.height);
+    let r = f32(tm_histogram[idx]);
+    let g = f32(tm_histogram[idx + plane]);
+    let b = f32(tm_histogram[idx + 2 * plane]);
+
+    // Normalize by the *average* density (total samples / pixel count) rather
+    // than total samples alone, so the scale stays sane across widget sizes
+    // and sample-dispatch rates. Buddhabrot density is extremely peaked (the
+    // brightest pixels run tens of times the average), so the compressive
+    // exponential tonemap only needs a small fraction of the average to reach
+    // full brightness at those peaks; 0.05 is a hand-tuned starting point,
+    // the exposure slider covers the rest.
+    let avg_density = max(u.total_samples / f32(u.width * u.height), 1.0e-6);
+    let scale = u.exposure * 0.05 / avg_density;
+    // Per-cap brightness, each already compressed to [0,1]. Nested caps mean
+    // r <= g <= b pointwise (every orbit counted in a smaller cap is also
+    // counted in every larger one), so fb alone is the full escaping-orbit
+    // density and fr picks out just the common, fast-escaping ones.
+    let fr = 1.0 - exp(-r * scale);
+    let fg = 1.0 - exp(-g * scale);
+    let fb = 1.0 - exp(-b * scale);
+
+    var col: vec3<f32>;
+    if u.palette == PALETTE_YELLOW {
+        // fr is *not* a good stand-alone brightness signal: with c sampled
+        // uniformly over the whole viewport, nearly every sample outside the
+        // set escapes within a handful of iterations and splats a couple of
+        // points near itself, so fr is a near-uniform wash across the entire
+        // image (not concentrated near the boundary the way fb is) — adding
+        // it directly (tried first, both raw and gamma-lifted) drags that
+        // wash up to full brightness and floods the background with solid
+        // colour. Instead use it as a *multiplicative* warm (yellow) tint on
+        // top of fb's brightness, so it only shows up where fb is already
+        // bright (i.e. real near-boundary density) and stays near-zero across
+        // the background (fb ≈ 0 there, so warmth * fb ≈ 0 regardless of fr).
+        col = vec3<f32>(
+            fb + fb * fr * 1.3,
+            fb + fb * fr * 0.6,
+            fb,
+        );
+    } else if u.palette == PALETTE_GRAYSCALE {
+        // fb is the full escaping-orbit density (the cumulative superset);
+        // reuse it directly as a single luminance channel.
+        col = vec3<f32>(fb, fb, fb);
+    } else {
+        col = vec3<f32>(fr, fg, fb); // classic: raw per-cap R/G/B
+    }
+    return vec4<f32>(clamp(col, vec3<f32>(0.0), vec3<f32>(1.0)), 1.0);
+}

src/shaders/colorize.wgsl

@@ -0,0 +1,197 @@
+// Colourise pass: map the iteration pass's per-pixel escape data (from
+// `mandelbrot.wgsl`'s `fs_data`) through the palette. This is the only
+// color-dependent step, so changing the palette / colour scale / offset (e.g.
+// colour cycling) re-runs just this cheap pass — the expensive perturbation
+// iteration in the data texture is reused untouched.
+//
+// The data texture holds, per texel: R = ci (palette parameter), G = DE
+// darkening factor, B = interior fraction (for boundary anti-aliasing). It is
+// the same resolution as this pass's target, so we read it with `textureLoad`
+// at the fragment's integer pixel coordinate (nearest — iteration data must not
+// be linearly filtered across escape boundaries).
+
+@group(0) @binding(0) var<uniform> u: Uniforms;
+@group(0) @binding(1) var data_tex: texture_2d<f32>;
+@group(0) @binding(2) var<uniform> lights: array<Light, 16>;
+
+@vertex
+fn vs_main(@builtin(vertex_index) idx: u32) -> @builtin(position) vec4<f32> {
+    return vec4<f32>(fullscreen_triangle_pos(idx), 0.0, 1.0);
+}
+
+fn shadow_fragment(pos: vec2<f32>) -> vec4<f32> {
+    let x = i32(pos.x);
+    let y = i32(pos.y);
+    let size = textureDimensions(data_tex);
+    let here = textureLoad(data_tex, vec2<i32>(x, y), 0);
+    if here.b != 0. {
+        return vec4<f32>(shadow_interior_color(), 1.0);
+    }
+    // Forward differences, except on the last column/row where x+1 / y+1
+    // is off the texture: fall back to a backward difference, mirrored
+    // (h0 + (h0 - h[-1])) so the slope keeps the sign normal_from_heights
+    // expects — plugging h[-1] in directly would flip the normal there.
+    let h0 = here.g;
+    var h1: f32;
+    if x + 1 < i32(size.x) {
+        h1 = textureLoad(data_tex, vec2<i32>(x + 1, y), 0).g;
+    } else {
+        h1 = 2.0 * h0 - textureLoad(data_tex, vec2<i32>(x - 1, y), 0).g;
+    }
+    var h2: f32;
+    if y + 1 < i32(size.y) {
+        h2 = textureLoad(data_tex, vec2<i32>(x, y + 1), 0).g;
+    } else {
+        h2 = 2.0 * h0 - textureLoad(data_tex, vec2<i32>(x, y - 1), 0).g;
+    }
+    let normal = normal_from_heights(h0, h1, h2);
+    return vec4<f32>(shadow_color(normal, here.r), 1.0);
+}
+
+@fragment
+fn fs_main(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
+    if u.shadow == 2u {
+        return ray_marching(pos);
+    } else if u.shadow == 1u {
+        return shadow_fragment(pos.xy);
+    } else {
+        let d = textureLoad(data_tex, vec2<i32>(i32(pos.x), i32(pos.y)), 0);
+        let ci = d.r;
+        let de = d.g;
+        let interior_frac = d.b;
+
+        var col = classic_color(ci, de);
+        // Anti-alias the set boundary: fade toward black by the fraction of the
+        // pixel's sub-samples that landed in the interior.
+        col = col * (1.0 - interior_frac);
+        return vec4<f32>(col, 1.0);
+    }
+}
+
+// Colour of rays that miss the fractal's footprint.
+const RAY_MISS: vec4<f32> = vec4<f32>(1.0, 0.0, 0.0, 1.0);
+
+// Per-frame constants of the raymarch, computed once per pixel in
+// `ray_marching` rather than on each of the up-to-100 `sdf` steps.
+struct MarchConsts {
+    size: vec2<f32>,
+    // (size.x / aspect_ratio, size.y): world xy -> texel scale.
+    to_texel: vec2<f32>,
+    size_i: vec2<i32>,
+    inv_size_y: f32,
+};
+
+fn sdf(pos: vec3<f32>, k: MarchConsts) -> f32 {
+    let texture_pos_f32 = pos.xy * k.to_texel;
+    let texture_pos = clamp(vec2<i32>(texture_pos_f32), vec2<i32>(0, 0), k.size_i - vec2<i32>(1, 1));
+
+    let to_texture = max(-min(texture_pos_f32, vec2(0.)), max(texture_pos_f32 - k.size, vec2(0.)));
+    let dist_to_texture = length(to_texture) * k.inv_size_y;
+
+    let px = textureLoad(data_tex, texture_pos, 0);
+    let de = (px.g * k.inv_size_y) * 0.5;
+    // Height is measured toward -z, the side the camera sits on (it looks
+    // along +z), so the terrain is solid on +z: interior plateau at z = 0,
+    // exterior sloping away from the camera as `de` grows.
+    let signed_z = -pos.z;
+    let z = max(signed_z, 0.);
+    var d: f32;
+    if px.b != 0. {
+        d = z;
+    } else {
+        d = min(sqrt(z * z + de * de), signed_z + 1. - exp(-de * 5.));
+    }
+    // Outside the texture footprint, `d` is the distance from the clamped
+    // point q on the footprint's edge. The terrain lies over the (convex)
+    // footprint, so |p - x|² ≥ |q - x|² + |p - q|² for every terrain point x:
+    // combine in quadrature (not by adding, which overshoots). p can't be in
+    // the solid out here, so a negative `d` counts as 0.
+    if dist_to_texture > 0. {
+        let d_pos = max(d, 0.);
+        return sqrt(d_pos * d_pos + dist_to_texture * dist_to_texture);
+    }
+    return d;
+}
+
+fn ray_marching(pos: vec4<f32>) -> vec4<f32> {
+    let size_i = vec2<i32>(textureDimensions(data_tex));
+    let size = vec2<f32>(size_i);
+    let aspect_ratio = u.screen_dim.x / u.screen_dim.y;
+    let k = MarchConsts(size, vec2<f32>(size.x / aspect_ratio, size.y), size_i, 1.0 / size.y);
+
+    let in_texture = vec2<f32>(
+        (pos.x / size.x) * 2. - 1.,
+        (pos.y / size.y) * 2. - 1.,
+    );
+
+    var world_pos = u.camera_inv_proj * vec4<f32>(in_texture, 0., 1.0);
+
+    let ray_origin = world_pos.xyz;
+    let ray_dir = u.camera_direction;
+
+    // Start where the ray crosses z = 0, the topmost possible surface (the
+    // camera pitch is clamped short of ±90°, so ray_dir.z > 0).
+    let start = ray_origin - ray_dir * (ray_origin.z / ray_dir.z);
+
+    // The terrain only exists over the footprint x in [0, aspect],
+    // y in [0, 1]: clip the ray's xy to it up front, so rays that miss it cost
+    // nothing and the rest start marching at its edge. A huge finite 1/d on
+    // an axis the ray doesn't move along (top-down, during the 2D <-> 3D
+    // transition) keeps the slab maths finite.
+    let inv = select(1.0 / ray_dir.xy, vec2<f32>(1e30), abs(ray_dir.xy) < vec2<f32>(1e-20));
+    let ta = -start.xy * inv;
+    let tb = (vec2<f32>(aspect_ratio, 1.0) - start.xy) * inv;
+    let t_leave = min(max(ta.x, tb.x), max(ta.y, tb.y));
+    var t = max(max(min(ta.x, tb.x), min(ta.y, tb.y)), 0.0);
+    if t >= t_leave {
+        return RAY_MISS;
+    }
+
+    // About 1/50 of a texel at typical sizes: tighter only adds steps
+    // without visibly moving the hit.
+    let dist_threshold = 0.00001;
+    // Rays grazing the exponential slope see a tiny `dist` for many steps in
+    // a row and would crawl along it until the step budget runs out. Force a
+    // step of at least half a texel (the height field is nearest-sampled, so
+    // nothing finer exists), and bisect back if that lands inside the solid.
+    let min_step = 0.5 * k.inv_size_y;
+    var hit = false;
+    var t_prev = t;
+    for (var i = 0u; i < 100u; i++) {
+        let dist = sdf(start + t * ray_dir, k);
+        if dist < dist_threshold {
+            hit = true;
+            if dist < 0. {
+                // Overshot: t_prev is outside, t inside. Refine the crossing.
+                var lo = t_prev;
+                var hi = t;
+                for (var j = 0u; j < 8u; j++) {
+                    let mid = 0.5 * (lo + hi);
+                    if sdf(start + mid * ray_dir, k) < dist_threshold {
+                        hi = mid;
+                    } else {
+                        lo = mid;
+                    }
+                }
+                t = hi;
+            }
+            break;
+        }
+        t_prev = t;
+        t += max(dist, min_step);
+        // Past the footprint's far edge: nothing left to hit.
+        if t >= t_leave {
+            break;
+        }
+    }
+    // Out of steps while still over the footprint: the ray is skimming the
+    // surface, so shade where it got to rather than reporting a miss.
+    if !hit && t < t_leave {
+        hit = true;
+    }
+    // Shade outside the loop, so its registers don't weigh on the march.
+    if !hit {
+        return RAY_MISS;
+    }
+    return shadow_fragment((start.xy + t * ray_dir.xy) * k.to_texel);
+}

src/shaders/common.wgsl

@@ -0,0 +1,55 @@
+// Shared helpers, concatenated into every shader at build time via
+// `concat!`/`include_str!` (see renderer.rs / buddhabrot.rs). Keep this file
+// free of anything that differs between pipelines (e.g. a `Uniforms` struct —
+// mandelbrot/colorize and buddhabrot each have their own shape) since every
+// shader gets the whole thing spliced in.
+
+// Fullscreen triangle vertex position: one triangle that covers the whole
+// viewport (cheaper than a quad's two), shared by every full-screen vertex
+// shader in this project.
+fn fullscreen_triangle_pos(idx: u32) -> vec2<f32> {
+    var verts = array<vec2<f32>, 3>(
+        vec2<f32>(-1.0, -1.0),
+        vec2<f32>(3.0, -1.0),
+        vec2<f32>(-1.0, 3.0),
+    );
+    return verts[idx];
+}
+
+// Complex multiply.
+fn cmul(a: vec2<f32>, b: vec2<f32>) -> vec2<f32> {
+    return vec2<f32>(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
+}
+
+// z^p for a complex exponent p, via the principal branch z^p = exp(p * ln z),
+// ln z = ln|z| + i*arg(z). z = 0 maps to 0 (the correct limit for the
+// Re(p) > 0 region the UI exposes; ln(0) would otherwise be -inf).
+fn cpow(z: vec2<f32>, p: vec2<f32>) -> vec2<f32> {
+    let r2 = dot(z, z);
+    if r2 < 1e-30 {
+        return vec2<f32>(0.0, 0.0);
+    }
+    let ln_r = 0.5 * log(r2);
+    let theta = atan2(z.y, z.x);
+    let mag = exp(p.x * ln_r - p.y * theta);
+    let ang = p.x * theta + p.y * ln_r;
+    return mag * vec2<f32>(cos(ang), sin(ang));
+}
+
+// Iteration formula selector, shared by the perturbation (mandelbrot.wgsl)
+// and direct (buddhabrot.wgsl) iteration paths. Must match `FractalKind` in
+// reference.rs.
+const KIND_MANDELBROT: u32 = 0u;
+const KIND_BURNING_SHIP: u32 = 1u;
+const KIND_TRICORN: u32 = 2u;
+const KIND_MULTIBROT: u32 = 3u;
+// Highest Multibrot power (the UI/CLI/share-link clamp in app.rs matches).
+// `bailout_sq` in app.rs shrinks the bailout with the power so z^p stays a
+// finite f32.
+const MULTIBROT_MAX_POWER: u32 = 20u;
+const KIND_CELTIC: u32 = 4u;
+const KIND_PERPENDICULAR: u32 = 5u;
+const KIND_BUFFALO: u32 = 6u;
+const KIND_PHOENIX: u32 = 7u;
+const KIND_LAMBDA: u32 = 8u;
+const KIND_COMPLEX_MULTIBROT: u32 = 9u;

src/shaders/iterate_uniforms.wgsl

@@ -0,0 +1,197 @@
+// Shared by mandelbrot.wgsl (writes the per-pixel data texture) and
+// colorize.wgsl (reads it): the iteration pass and the colour remap pass
+// must agree on both the uniform layout and the palette function.
+
+// Must match the Rust `Uniforms` struct in renderer.rs field-for-field,
+// including padding.
+struct Uniforms {
+    span: vec2<f32>,
+    max_iter: u32,
+    ref_len: u32,
+    color_offset: f32,
+    color_scale: f32,
+    bailout_sq: f32,
+    is_julia: u32,
+    palette_id: u32,
+    shadow_palette_id: u32,
+    aa_level: u32,
+    // Iteration formula (see the KIND_* constants in common.wgsl).
+    kind: u32,
+    // Exponent for the Multibrot kind.
+    power: u32,
+    // Kind-switch morph: the kind blended *from* (see morph_w).
+    morph_from: u32,
+    dc_offset: vec2<f32>,
+    // Distortion constant p for the Phoenix map (z^2 + c + p*z_{n-1}); unused
+    // by other kinds. Placed by dc_offset so both vec2s stay 8-byte aligned.
+    phoenix_p: vec2<f32>,
+    // Distortion constant l for the Lambda map (l*z(1 - z_{n-1})); unused
+    // by other kinds.
+    lambda_l: vec2<f32>,
+    // Complex exponent for the Complex Multibrot kind (z^power + c); unused
+    // by other kinds.
+    complex_power: vec2<f32>,
+    // 0 = escape-time coloring, 1 = distance-estimation shading.
+    de_coloring: u32,
+    // 0 = classic colors, 1 = shadows, 2 = 3D raymarching rendering
+    shadow: u32,
+    // camera direction vector
+    camera_direction: vec3<f32>,
+    // Number of live entries at the start of `lights` (fills the vec3's tail
+    // padding slot).
+    light_count: u32,
+    // inverse of the camera's view-projection matrix, for reconstructing a
+    // world-space ray origin per pixel in the raymarcher
+    camera_inv_proj: mat4x4<f32>,
+    // Screen dimensions
+    screen_dim: vec2<f32>,
+    // Kind-switch morph weight: each step is (1 - w)*f_kind + w*f_morph_from;
+    // 0 = no morph. Only read by MORPH pipelines (see mandelbrot.wgsl).
+    morph_w: f32,
+    // Deep views: binary exponent E of the view scale. `span` and `dc_offset`
+    // are uploaded multiplied by 2^-E so they stay in f32's range; 0 = not
+    // deep (plain f32 values). Only read by DEEP pipelines (mandelbrot.wgsl).
+    scale_exp: i32,
+    // Complex binomial coefficients C(complex_power, k) for k = 1..16, two per
+    // vec4 (k odd in .xy, k even in .zw), for the Complex Multibrot delta
+    // series. Precomputed on the CPU since they only depend on the power.
+    cm_coef: array<vec4<f32>, 8>,
+};
+
+// Smooth cyclic palettes (Inigo Quilez cosine palettes), selected by id.
+fn palette(id: u32, t: f32) -> vec3<f32> {
+    if id == 4u {
+        return vec3<f32>(t, t, t); // grayscale
+    }
+    let a = vec3<f32>(0.5, 0.5, 0.5);
+    let b = vec3<f32>(0.5, 0.5, 0.5);
+    var c = vec3<f32>(1.0, 1.0, 1.0);
+    var d = vec3<f32>(0.00, 0.10, 0.20); // 0: amber / blue
+    if id == 1u {
+        d = vec3<f32>(0.00, 0.33, 0.67); // rainbow
+    } else if id == 2u {
+        d = vec3<f32>(0.30, 0.20, 0.20); // warm ember
+    } else if id == 3u {
+        c = vec3<f32>(1.0, 1.0, 0.5);
+        d = vec3<f32>(0.80, 0.90, 0.30); // lime / magenta
+    }
+    return a + b * cos(6.28318530718 * (c * t + d));
+}
+
+// Classic (non-shadow) escape colouring: palette lookup at the smoothed
+// iteration count `ci`, darkened by the distance-estimate factor `de`
+// (sqrt-compressed so the darkening falls off more gently near the
+// boundary). Shared by the colourise pass's classic branch (colorize.wgsl,
+// applied to an already-averaged data texel) and the PNG-export pass
+// (mandelbrot.wgsl's `fs_color`, applied per sub-sample pre-AA) — the two
+// places a fully escaped point is turned into a final pixel colour.
+fn classic_color(ci: f32, de: f32) -> vec3<f32> {
+    let t = fract(ci * u.color_scale + u.color_offset);
+    return palette(u.palette_id, t) * sqrt(de);
+}
+
+// A single directional light, built on the CPU from the UI's light list
+// (`GpuLight` in lights.rs): `dir` is the unit direction toward the light
+// (precomputed from azimuth/altitude so the shader does no trig), `color` a
+// packed RGBA8 whose alpha doubles as intensity. Only the first
+// `u.light_count` entries are live, all with a non-zero colour. Each shader
+// that binds a `lights: array<Light, 16>` uniform (colorize.wgsl,
+// mandelbrot.wgsl's export shadow path) uses this same layout.
+struct Light {
+    dir: vec3<f32>,
+    color: u32,
+};
+
+// Lambertian term for a unit `light` direction.
+fn compute_light(normal: vec3<f32>, light: vec3<f32>) -> vec3<f32> {
+    return vec3<f32>(max(0., dot(normal, light)));
+}
+
+fn uncharted2tonemap(x: vec3<f32>) -> vec3<f32> {
+    let A = 0.15; // Shoulder strength
+    let B = 0.50; // Linear strength
+    let C = 0.10; // Linear angle
+    let D = 0.20; // Toe strength
+    let E = 0.02; // Toe numerator / shoarder angle/etc.
+    let F = 0.30; // Toe denominator
+
+    return ((x * (A * x + C * B) + D * E) / (x * (A * x + B) + D * F)) - E / F;
+}
+
+fn filmic(color: vec3<f32>, white_point: f32) -> vec3<f32> {
+    let exposure_bias = 2.0;
+    let curr = uncharted2tonemap(color * exposure_bias);
+
+    // Valeur blanche maximale de référence
+    let white_scale = vec3(1.0) / uncharted2tonemap(vec3(white_point));
+    return curr * white_scale;
+}
+
+fn s(color: vec3<f32>, k: f32, c: f32) -> vec3<f32> {
+    return 1. / (1. + exp(-k * (color - c)));
+}
+
+fn contrast(color: vec3<f32>, k: f32, c: f32) -> vec3<f32> {
+    let color_c = s(color, k, c);
+
+    return (color_c - s(vec3<f32>(0), k, c)) / (s(vec3<f32>(1), k, c) - s(vec3<f32>(0), k, c));
+}
+
+// Surface normal from three height samples (`h0` at the pixel, `h1` one pixel
+// to the right, `h2` one pixel down), treating DE as a height field. Only the
+// differences matter, so callers don't need to pass pixel coordinates — a
+// texture-backed caller (colorize.wgsl) and a live-sampled caller
+// (mandelbrot.wgsl's export shadow path) can share this.
+fn normal_from_heights(h0: f32, h1: f32, h2: f32) -> vec3<f32> {
+    let d0 = vec3<f32>(0.0, 0.0, h0);
+    let d1 = vec3<f32>(1.0, 0.0, h1);
+    let d2 = vec3<f32>(0.0, 1.0, h2);
+    return normalize(cross(d1 - d0, d2 - d0));
+}
+
+// Shade a DE-derived surface normal per `u.shadow_palette_id`: 0 = grayscale
+// key light, 1 = red/blue two-tone, 2 = the user's custom `lights` list,
+// 3 = the classic escape-time palette at `ci` (the smoothed iteration count),
+// lit by the grayscale key light.
+// Shared by the interactive shadow pass (colorize.wgsl) and the PNG-export
+// shadow path (mandelbrot.wgsl's `fs_color`), which must render identically.
+fn shadow_color(normal: vec3<f32>, ci: f32) -> vec3<f32> {
+    var color: vec3<f32>;
+    if u.shadow_palette_id == 0u {
+        color = compute_light(normal, vec3<f32>(0.57735027, 0.57735027, 0.57735027)) + vec3<f32>(0.58, 0.85, 1.) * 0.2;
+
+        color = filmic(color, 2.5);
+        color = contrast(color, 4., 0.67);
+    } else if u.shadow_palette_id == 1u {
+        color = compute_light(normal, vec3<f32>(0., 0.70710678, 0.70710678)) * vec3<f32>(1., 0.5, 0.5) + compute_light(normal, vec3<f32>(0.70710678, 0., 0.70710678)) * vec3<f32>(0.5, 1., 1.);
+
+        color = filmic(color, 4.2);
+    } else if u.shadow_palette_id == 3u {
+        // No DE darkening as in `classic_color`: in shadow/3D modes the DE
+        // is a height (unclamped, not capped at 1), and the lighting already
+        // shows the relief.
+        let t = fract(ci * u.color_scale + u.color_offset);
+        let ambient = 0.25;
+        let light = compute_light(normal, vec3<f32>(0.57735027, 0.57735027, 0.57735027));
+        color = palette(u.palette_id, t) * (ambient + (1.0 - ambient) * light);
+    } else {
+        color = vec3<f32>(0);
+        let light_count = min(u.light_count, 16u);
+        for (var i = 0u; i < light_count; i++) {
+            let light_color = unpack4x8unorm(lights[i].color);
+            color += compute_light(normal, lights[i].dir) * light_color.xyz * light_color.a;
+        }
+
+        color = filmic(color, 1. + f32(light_count));
+    }
+    return color;
+}
+
+// Colour of an interior (non-escaped) pixel in shadow/3D modes: black under
+// the classic palette, like classic 2D mode, otherwise a dark gray plateau.
+fn shadow_interior_color() -> vec3<f32> {
+    if u.shadow_palette_id == 3u {
+        return vec3<f32>(0.0);
+    }
+    return vec3<f32>(0.1);
+}

src/shaders/lipschitz.wgsl

@@ -0,0 +1,121 @@
+// Distance field for the shadow and 3D views of kinds whose map is
+// discontinuous (Complex Multibrot's principal-branch z^p). The per-pixel
+// DE, |z|·ln|z|/|dz| = G/|G'|, is only a distance when the potential G is
+// continuous. Across a branch-cut preimage G jumps (|z| jumps by
+// e^(2π·Im p)), each side's DE describes the set as continued on its own
+// branch: seams in shadow mode, walls in the raymarched terrain. A true
+// distance to the set is continuous, so this rebuilds one from the pixels that are unambiguously
+// next to the set ("seeds": interior texels, and exterior texels whose DE is
+// below SEED_DE, i.e. within about a pixel of it):
+//     h(x) = min over seeds y of  DE(y) + DIST_SLOPE·|x - y|
+// computed by jump flooding: `fs_seed` marks seeds, `fs_jump` runs with
+// `step` halving from about half the texture size down to 1 (plus one more
+// step-1 pass), each texel keeping the best seed among itself and its 8
+// neighbours at ±step, and `fs_compose` writes the result, eased by
+// `ease_distance`, as the data texture's G channel. Seeds are carried as coordinates, so the distance is
+// Euclidean rather than an 8-direction chamfer approximation.
+//
+// The set only counts where it's in view: next to the image edge, set just
+// outside it is missed and the height there reads a bit high.
+//
+// Texel layout of the seed textures: (seed x, seed y, seed DE, 1), or all 0
+// for "no seed yet". R (palette parameter) and B (interior fraction) of the
+// data texture pass through untouched.
+
+struct LipschitzStep {
+    step: i32,
+    _pad0: i32,
+    _pad1: i32,
+    _pad2: i32,
+};
+
+@group(0) @binding(0) var data_tex: texture_2d<f32>;
+@group(0) @binding(1) var seed_tex: texture_2d<f32>;
+@group(0) @binding(2) var<uniform> ls: LipschitzStep;
+
+// DE units per texel of a true distance: DE is in units of `pixel_size`,
+// the texel's (|dx| + |dy|) footprint, i.e. sqrt(2) texels.
+const DIST_SLOPE: f32 = 0.70710678;
+// Exterior texels with a DE below this (in DE units) are seeds.
+const SEED_DE: f32 = 1.0;
+
+@vertex
+fn vs_main(@builtin(vertex_index) idx: u32) -> @builtin(position) vec4<f32> {
+    return vec4<f32>(fullscreen_triangle_pos(idx), 0.0, 1.0);
+}
+
+@fragment
+fn fs_seed(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
+    let p = vec2<i32>(pos.xy);
+    let d = textureLoad(data_tex, p, 0);
+    if d.b != 0.0 {
+        return vec4<f32>(vec2<f32>(p), 0.0, 1.0);
+    }
+    if d.g < SEED_DE {
+        return vec4<f32>(vec2<f32>(p), d.g, 1.0);
+    }
+    return vec4<f32>(0.0);
+}
+
+// Height at `p` through seed `s` (a seed texel), or +inf for "no seed".
+fn through(p: vec2<i32>, s: vec4<f32>) -> f32 {
+    if s.a == 0.0 {
+        return 3.0e38;
+    }
+    return s.z + DIST_SLOPE * distance(vec2<f32>(p), s.xy);
+}
+
+@fragment
+fn fs_jump(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
+    let p = vec2<i32>(pos.xy);
+    let hi = vec2<i32>(textureDimensions(seed_tex)) - vec2<i32>(1, 1);
+    let st = ls.step;
+    var best = textureLoad(seed_tex, p, 0);
+    var best_h = through(p, best);
+    for (var dy = -1; dy <= 1; dy++) {
+        for (var dx = -1; dx <= 1; dx++) {
+            if dx == 0 && dy == 0 {
+                continue;
+            }
+            let q = p + st * vec2<i32>(dx, dy);
+            if any(q < vec2<i32>(0, 0)) || any(q > hi) {
+                continue;
+            }
+            let s = textureLoad(seed_tex, q, 0);
+            let h = through(p, s);
+            if h < best_h {
+                best = s;
+                best_h = h;
+            }
+        }
+    }
+    return best;
+}
+
+// Scale of `ease_distance`, in screen heights.
+const EASE_K: f32 = 0.02;
+
+// Concave easing of the distance field `h` (DE units, `size_y` texels
+// tall): K·ln(1 + x/K) in screen heights, the unit `sdf` in colorize.wgsl
+// reads. Slope 1 at the set, flattening far from it, so the terrain rises
+// steeply out of the set and then levels off. The slope never exceeds 1,
+// so the field stays a valid (conservative) distance for the sphere tracer.
+fn ease_distance(h: f32, size_y: f32) -> f32 {
+    return EASE_K * log(1.0 + h / (size_y * EASE_K)) * size_y;
+}
+
+@fragment
+fn fs_compose(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
+    let p = vec2<i32>(pos.xy);
+    let d = textureLoad(data_tex, p, 0);
+    if d.b != 0.0 {
+        return d;
+    }
+    // Not min(h, DE): that keeps the too-low side of every jump, so the
+    // walls come back as shards.
+    let h = through(p, textureLoad(seed_tex, p, 0));
+    if h >= 3.0e38 {
+        return d; // no set anywhere in view: keep the DE
+    }
+    return vec4<f32>(d.r, ease_distance(h, f32(textureDimensions(data_tex).y)), d.b, d.a);
+}

src/view.rs

@@ -1,61 +1,304 @@
 //! Camera / view state over the complex plane.
 //!
-//! The center is stored in arbitrary precision (`FBig`) — this is what lets us
+//! The center is stored in arbitrary precision ([`Big`]) — this is what lets us
-//! zoom far past f64's ~1e13x limit. The pixel *scale* stays `f64`: even at
+//! zoom far past f64's ~1e13x limit. The pixel *scale* is a [`Scale`]: an
-//! 10^30x zoom the scale is ~1e-33, comfortably inside f64's range. Only the
+//! f64 mantissa with its own `i32` binary exponent, so it isn't bound by
-//! center needs the extra digits.
+//! f64's ~1e-308 range either (the floor, `Scale::MIN`, only keeps the GPU's
+//! i32 exponent arithmetic far from overflow). Once a pixel is smaller than
+//! `DEEP_PIXEL_SIZE` the GPU switches to rescaled deltas (see `needs_deep`),
+//! since f32 alone bottoms out near 1e-38.
 
 use core::str::FromStr;
 
-use dashu_float::round::mode::HalfAway;
+pub use crate::bignum::Big;
-use dashu_float::{DBig, FBig};
-
-/// Arbitrary-precision binary float (base 2, round-half-away). One coordinate.
-pub type Big = FBig<HalfAway, 2>;
 
 /// Half-height (complex units) of the default view; also the zoom-1 reference.
 pub const DEFAULT_HALF_HEIGHT: f64 = 1.25;
 
+/// Below this pixel size (complex units per pixel) the GPU renders with the
+/// deep pipeline, whose per-pixel deltas start out as an f32 mantissa times
+/// `2^scale_exp`. Plain f32 stays exact as long as the smallest per-pixel
+/// offsets (a quarter pixel, for the AA grid) are normal floats (>= 2^-126),
+/// i.e. down to 2^-124 per pixel. Measured: pixel-identical to the deep path
+/// down to 2^-124 (no AA), first errors at 2^-126, all black by 2^-136. The
+/// deep path is slower, so the switch is as late as that allows, with two
+/// binades of margin.
+pub const DEEP_PIXEL_SIZE: f64 = 1.0 / (1u128 << 122) as f64; // 2^-122
+
+/// Whether a view rendered `height_px` pixels tall needs the deep pipeline
+/// (see `DEEP_PIXEL_SIZE`).
+pub fn needs_deep(half_height: Scale, height_px: f64) -> bool {
+    half_height.mul_f64(2.0 / height_px.max(1.0)) < Scale::from_f64(DEEP_PIXEL_SIZE)
+}
+
+/// Binary exponent `E` of the deep view scale: `floor(log2(half_height))`,
+/// so the rescaled span is in `[2, 4)`. Never 0, which means "not deep"
+/// (see `Uniforms::scale_exp`).
+pub fn deep_scale_exp(half_height: Scale) -> i32 {
+    let e = half_height.exponent();
+    if e == 0 { -1 } else { e }
+}
+
+/// `x * 2^k` for any `k`, saturating to 0 / infinity like the true value
+/// would (`powi` alone overflows at 2^±1024 even when the product fits).
+fn ldexp(mut x: f64, mut k: i32) -> f64 {
+    while k > 1000 {
+        x *= 2f64.powi(1000);
+        k -= 1000;
+        if x.is_infinite() || x == 0.0 {
+            return x;
+        }
+    }
+    while k < -1000 {
+        x *= 2f64.powi(-1000);
+        k += 1000;
+        if x == 0.0 || x.is_infinite() {
+            return x;
+        }
+    }
+    x * 2f64.powi(k)
+}
+
+/// A positive real with f64 precision and an `i32` binary exponent:
+/// `m · 2^e`, `m` in `[1, 2)`. The view's half-height (and the pixel size
+/// derived from it) is one of these, so zoom isn't bound by f64's range.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct Scale {
+    m: f64,
+    e: i32,
+}
+
+impl Scale {
+    /// Deepest scale the view can reach: 2^-(2^20) (about 1e-315653). Far
+    /// past anything a reference orbit can practically be computed for; it
+    /// only keeps the shader's i32 exponent sums (scale × degree) from
+    /// overflowing.
+    pub const MIN: Scale = Scale {
+        m: 1.0,
+        e: -(1 << 20),
+    };
+
+    /// `m · 2^e`, normalized. Non-positive or NaN input gives `MIN`.
+    pub fn from_parts(m: f64, e: i32) -> Self {
+        if m.is_nan() || m <= 0.0 {
+            return Self::MIN;
+        }
+        if m.is_infinite() {
+            return Scale {
+                m: 1.0,
+                e: i32::MAX / 2,
+            };
+        }
+        // Bring m into [1, 2) through its own binary exponent (exact).
+        let k = m.log2().floor() as i32;
+        let mut m = ldexp(m, -k);
+        let mut e = e.saturating_add(k);
+        // log2 can round across a power of two.
+        if m >= 2.0 {
+            m /= 2.0;
+            e = e.saturating_add(1);
+        } else if m < 1.0 {
+            m *= 2.0;
+            e = e.saturating_sub(1);
+        }
+        Scale { m, e }.max(Self::MIN)
+    }
+
+    pub fn from_f64(x: f64) -> Self {
+        Self::from_parts(x, 0)
+    }
+
+    /// `2^l`.
+    pub fn from_log2(l: f64) -> Self {
+        let e = l.floor();
+        Self::from_parts((l - e).exp2(), e as i32)
+    }
+
+    /// The value as an f64 (0 or infinity outside its range).
+    pub fn to_f64(self) -> f64 {
+        ldexp(self.m, self.e)
+    }
+
+    /// `self · 2^k` as an f64: the value in units of `2^-k`.
+    pub fn scaled_f64(self, k: i32) -> f64 {
+        ldexp(self.m, self.e.saturating_add(k))
+    }
+
+    /// `floor(log2(self))`.
+    pub fn exponent(self) -> i32 {
+        self.e
+    }
+
+    pub fn log2(self) -> f64 {
+        self.m.log2() + self.e as f64
+    }
+
+    pub fn log10(self) -> f64 {
+        self.log2() * core::f64::consts::LOG10_2
+    }
+
+    /// `self · f` (`f > 0`).
+    pub fn mul_f64(self, f: f64) -> Self {
+        Self::from_parts(self.m * f, self.e)
+    }
+
+    /// `self / other`, as an f64.
+    pub fn ratio(self, other: Scale) -> f64 {
+        ldexp(self.m / other.m, self.e.saturating_sub(other.e))
+    }
+
+    pub fn max(self, other: Scale) -> Self {
+        if other > self { other } else { self }
+    }
+
+    pub fn min(self, other: Scale) -> Self {
+        if other < self { other } else { self }
+    }
+
+    pub fn clamp(self, lo: Scale, hi: Scale) -> Self {
+        self.max(lo).min(hi)
+    }
+
+    /// `f · self` as an exact `Big` at `bits` of precision (`f` any f64).
+    pub fn big_times(self, f: f64, bits: usize) -> Big {
+        big_from_f64(f * self.m, bits) << self.e as isize
+    }
+
+    /// Exact binary value as a `Big`.
+    fn to_big(self) -> Big {
+        big_from_f64(self.m, 53) << self.e as isize
+    }
+}
+
+impl PartialOrd for Scale {
+    fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
+        // Normalized and positive: the exponent decides, then the mantissa.
+        Some(self.e.cmp(&other.e).then(self.m.partial_cmp(&other.m)?))
+    }
+}
+
+impl core::fmt::Display for Scale {
+    /// Scientific notation, `1.5e-20` / `3.7e-4000`. The precision flag
+    /// (`{:.4}`) sets mantissa digits after the point; without it, enough
+    /// digits to parse back to the same value.
+    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
+        let x = self.to_f64();
+        if x.is_normal() {
+            return match f.precision() {
+                Some(p) => write!(f, "{x:.p$e}"),
+                None => write!(f, "{x:e}"),
+            };
+        }
+        // Out of f64's range: round the exact decimal expansion instead.
+        let big = self.to_big();
+        let sci = |sig: usize, pad: Option<usize>| {
+            let parts = big.to_decimal_parts(sig);
+            let digits = if parts.digits.is_empty() {
+                "0"
+            } else {
+                &parts.digits
+            };
+            // value = 0.digits · 10^exp10; move the point after the first digit.
+            let exp10 = parts.exp10 - 1;
+            let (head, tail) = digits.split_at(1);
+            let tail = match pad {
+                Some(p) => format!("{tail:0<p$}"),
+                None => tail.to_string(),
+            };
+            if tail.is_empty() {
+                format!("{head}e{exp10}")
+            } else {
+                format!("{head}.{tail}e{exp10}")
+            }
+        };
+        match f.precision() {
+            Some(p) => f.write_str(&sci(p + 1, Some(p))),
+            None => {
+                // Like `{:e}` on f64: the shortest string that parses back.
+                let s = (1..17)
+                    .map(|sig| sci(sig, None))
+                    .find(|s| s.parse::<Scale>() == Ok(*self))
+                    .unwrap_or_else(|| sci(17, None));
+                f.write_str(&s)
+            }
+        }
+    }
+}
+
+impl FromStr for Scale {
+    type Err = ();
+
+    /// Parses any positive decimal (`1.25`, `1.5e-20`, `3.7e-4000`), rounding
+    /// to the nearest f64 mantissa. Values past `MIN` clamp to it.
+    fn from_str(s: &str) -> Result<Self, ()> {
+        let s = s.trim();
+        if let Ok(x) = s.parse::<f64>()
+            && x.is_normal()
+        {
+            return if x > 0.0 {
+                Ok(Self::from_f64(x))
+            } else {
+                Err(())
+            };
+        }
+        // Too small (or large) for f64: go through an exact decimal.
+        let bin = Big::from_decimal_str(s, 64).ok_or(())?;
+        if bin.is_negative() {
+            return Err(());
+        }
+        let top = bin.log2_floor().ok_or(())?;
+        let m = (bin >> top).to_f64();
+        let e = top.clamp(i32::MIN as isize, i32::MAX as isize) as i32;
+        Ok(Self::from_parts(m, e))
+    }
+}
+
 /// Guard bits added on top of the zoom-dictated precision.
 const GUARD_BITS: usize = 48;
-/// Upper bound on center precision (f32 GPU perturbation degrades long before
+/// Upper bound on center precision: what `Scale::MIN` needs. Only a guard
-/// this; the cap just prevents pathological allocation).
+/// against pathological input; the reference orbit is impractically slow
-const MAX_PRECISION_BITS: usize = 2048;
+/// long before this.
+pub const MAX_PRECISION_BITS: usize = (1 << 20) + GUARD_BITS;
 
 #[derive(Clone, Debug)]
 pub struct ViewState {
     pub center_re: Big,
     pub center_im: Big,
     /// Half the view height in complex-plane units. Zooming in shrinks this.
-    pub half_height: f64,
+    pub half_height: Scale,
 }
 
 impl Default for ViewState {
     fn default() -> Self {
-        let bits = precision_for(DEFAULT_HALF_HEIGHT);
+        let bits = precision_for(Scale::from_f64(DEFAULT_HALF_HEIGHT));
         Self {
             center_re: big_from_f64(-0.5, bits),
             center_im: big_from_f64(0.0, bits),
-            half_height: DEFAULT_HALF_HEIGHT,
+            half_height: Scale::from_f64(DEFAULT_HALF_HEIGHT),
         }
     }
 }
 
 impl ViewState {
     /// Complex-plane span (width, height) for the given pixel aspect ratio.
-    pub fn span(&self, aspect: f64) -> (f64, f64) {
+    pub fn span(&self, aspect: f64) -> (Scale, Scale) {
-        let h = self.half_height * 2.0;
+        let h = self.half_height.mul_f64(2.0);
-        (h * aspect, h)
+        (h.mul_f64(aspect), h)
     }
 
     /// Complex-plane units per pixel, given the viewport height in pixels.
-    pub fn complex_per_pixel(&self, height_px: f64) -> f64 {
+    pub fn complex_per_pixel(&self, height_px: f64) -> Scale {
-        (self.half_height * 2.0) / height_px
+        self.half_height.mul_f64(2.0 / height_px)
     }
 
-    /// Current magnification relative to the default view.
+    /// log10 of the current magnification relative to the default view.
-    pub fn magnification(&self) -> f64 {
+    pub fn magnification_log10(&self) -> f64 {
-        DEFAULT_HALF_HEIGHT / self.half_height
+        DEFAULT_HALF_HEIGHT.log10() - self.half_height.log10()
+    }
+
+    /// Current zoom level.
+    pub fn zoom(&self) -> Scale {
+        self.half_height
     }
 
     /// Bits of precision the center currently needs for this zoom level.
@@ -68,10 +311,10 @@ impl ViewState {
     pub fn sync_precision(&mut self) {
         let bits = self.precision_bits();
         if self.center_re.precision() < bits {
-            self.center_re = self.center_re.clone().with_precision(bits).value();
+            self.center_re = self.center_re.clone().with_precision(bits);
         }
         if self.center_im.precision() < bits {
-            self.center_im = self.center_im.clone().with_precision(bits).value();
+            self.center_im = self.center_im.clone().with_precision(bits);
         }
     }
 
@@ -81,8 +324,8 @@ impl ViewState {
         let cpp = self.complex_per_pixel(height_px);
         let bits = self.precision_bits();
         // Grab-and-drag: moving the mouse right shows content to the left.
-        self.center_re = &self.center_re - &big_from_f64(dx * cpp, bits);
+        self.center_re = &self.center_re - &cpp.big_times(dx, bits);
-        self.center_im = &self.center_im - &big_from_f64(dy * cpp, bits); // y-down -> imag-up
+        self.center_im = &self.center_im - &cpp.big_times(dy, bits);
     }
 
     /// Zoom by `factor` (<1 zooms in) keeping the complex point currently under
@@ -95,14 +338,14 @@ impl ViewState {
         // The cursor's complex offset from the center is (off * cpp). Keeping it
         // fixed while scaling the view by `factor` moves the center by
         // off * cpp * (1 - factor). (Derivation: new_c = fixed + (c-fixed)*f.)
-        let k = cpp * (1.0 - factor);
+        let k = 1.0 - factor;
-        self.center_re = &self.center_re + &big_from_f64(off_x * k, bits);
+        self.center_re = &self.center_re + &cpp.big_times(off_x * k, bits);
-        self.center_im = &self.center_im + &big_from_f64(off_y * k, bits); // y flip
+        self.center_im = &self.center_im + &cpp.big_times(off_y * k, bits);
-        self.half_height *= factor;
+        self.half_height = self.half_height.mul_f64(factor);
     }
 
     /// Build a view from full-precision center coordinates and a half-height.
-    pub fn with_center(center_re: Big, center_im: Big, half_height: f64) -> Self {
+    pub fn with_center(center_re: Big, center_im: Big, half_height: Scale) -> Self {
         let mut v = Self {
             center_re,
             center_im,
@@ -116,36 +359,253 @@ impl ViewState {
 /// Parse a decimal string (any number of digits) losslessly into a `Big` with at
 /// least `bits` of precision. Used for share links and debug view specs.
 pub fn big_from_decimal_str(s: &str, bits: usize) -> Option<Big> {
-    let dec = DBig::from_str(s.trim()).ok()?;
+    Big::from_decimal_str(s, bits)
-    Some(dec.with_base_and_precision::<2>(bits.max(53)).value())
+}
+
+/// Parse a "re,im,half_height[,iterations]" spec (re/im decimal, parsed at
+/// full precision) into a view and an optional iteration count. Shared by
+/// `FractalApp::apply_view_spec` (the `--view` CLI flag) and headless
+/// animation's `--to-view`.
+pub fn parse_view_spec(spec: &str) -> Option<(ViewState, Option<u32>)> {
+    let parts: Vec<&str> = spec.split(',').collect();
+    if parts.len() < 3 {
+        return None;
+    }
+    let half_height = parse_half_height_spec(parts[2])?;
+    let bits = precision_for(half_height);
+    let re = big_from_decimal_str(parts[0], bits)?;
+    let im = big_from_decimal_str(parts[1], bits)?;
+    let iterations = parts.get(3).and_then(|s| s.trim().parse::<u32>().ok());
+    Some((ViewState::with_center(re, im, half_height), iterations))
+}
+
+/// Parse a half_height spec. Shared by
+/// `FractalApp::apply_half_height_spec` (the `--zoom` CLI flag) and headless
+/// animation's `--to-zoom`.
+pub fn parse_half_height_spec(spec: &str) -> Option<Scale> {
+    spec.parse::<Scale>().ok()
+}
+/// Parse a "re,im" spec (re/im decimal, parsed at
+/// full precision) into a view. Shared by
+/// `FractalApp::apply_re_im_spec` (the `--position` CLI flag) and headless
+/// animation's `--to-position`.
+pub fn parse_re_im_spec(spec: &str, bits: usize) -> Option<(Big, Big)> {
+    let parts: Vec<&str> = spec.split(',').collect();
+    if parts.len() != 2 {
+        return None;
+    }
+    let re = big_from_decimal_str(parts[0], bits)?;
+    let im = big_from_decimal_str(parts[1], bits)?;
+    Some((re, im))
+}
+
+/// Interpolate between two views for an animation frame, `t` in `[0, 1]`.
+/// The half-height interpolates geometrically (log-linear), since zoom depth
+/// spans many decades and a linear sweep would crawl at the start and blow
+/// past the target at the end. The center has to shrink its offset from the
+/// target at that *same* geometric rate: blending it linearly in `t` instead
+/// barely moves it while the view is still huge (early frames), so the
+/// target stays effectively off-screen — offset/half_height ratio blows up —
+/// for nearly the whole animation, and only lands on `to`'s center in the
+/// literal last frame where `t == 1` forces an exact match. `g(t)` below
+/// tracks the same `q^t` decay used for `half_height` (keeping the
+/// offset/half_height ratio roughly constant, i.e. the target's on-screen
+/// position steady) but is shifted so it lands on exactly 1 at `t = 0` and
+/// exactly 0 at `t = 1`.
+///
+/// With `d = log2(q)`, `g = q^t · (1 - q^(1-t)) / (1 - q)`, all in `Scale`
+/// / `expm1` form: zooming in by more than f64's range, `q` (and `q^t`)
+/// underflow, yet `g · (from - to)` must keep tracking the half-height.
+pub fn interpolate_view(from: &ViewState, to: &ViewState, t: f64) -> ViewState {
+    let (l0, l1) = (from.half_height.log2(), to.half_height.log2());
+    let d = l1 - l0;
+    let half_height = if t <= 0.0 {
+        from.half_height
+    } else if t >= 1.0 {
+        to.half_height
+    } else {
+        Scale::from_log2(l0 + t * d)
+    };
+    let bits = precision_for(half_height);
+    let ln2 = core::f64::consts::LN_2;
+    let g_big = if d.abs() < 1e-12 {
+        big_from_f64(1.0 - t, bits)
+    } else if d < 0.0 {
+        // Zooming in: q^t may be far below f64's range, keep it as a Scale.
+        let f = ((1.0 - t) * d * ln2).exp_m1() / (d * ln2).exp_m1();
+        Scale::from_log2(t * d).big_times(f, bits)
+    } else {
+        // Zooming out: g = (1 - q^(t-1)) / (1 - q^-1), every term bounded.
+        big_from_f64(((t - 1.0) * d * ln2).exp_m1() / (-d * ln2).exp_m1(), bits)
+    };
+    let re0 = from.center_re.clone().with_precision(bits);
+    let im0 = from.center_im.clone().with_precision(bits);
+    let re1 = to.center_re.clone().with_precision(bits);
+    let im1 = to.center_im.clone().with_precision(bits);
+    let center_re = &re1 + &(&(&re0 - &re1) * &g_big);
+    let center_im = &im1 + &(&(&im0 - &im1) * &g_big);
+    ViewState::with_center(center_re, center_im, half_height)
+}
+
+#[cfg(not(target_arch = "wasm32"))]
+pub fn interpolate_f64(from: f64, to: f64, t: f64) -> f64 {
+    from + (to - from) * t
 }
 
 /// Render a `Big` as a decimal string with `sig_digits` significant digits.
 pub fn big_to_decimal_str(x: &Big, sig_digits: usize) -> String {
-    let dec = x
+    x.to_decimal_string(sig_digits)
-        .to_decimal()
-        .value()
-        .with_precision(sig_digits.max(1))
-        .value();
-    format!("{dec}")
 }
 
 /// Precision (bits) needed to resolve the center at a given half-height.
-pub fn precision_for(half_height: f64) -> usize {
+pub fn precision_for(half_height: Scale) -> usize {
     // We need enough bits to distinguish points a pixel apart, i.e. roughly
     // log2(1 / half_height) significant bits, plus a guard margin.
-    let zoom_bits = if half_height > 0.0 && half_height.is_finite() {
+    let zoom_bits = (-half_height.log2()).ceil().max(0.0) as usize;
-        (-half_height.log2()).ceil().max(0.0) as usize
-    } else {
-        0
-    };
     (zoom_bits + GUARD_BITS).clamp(53, MAX_PRECISION_BITS)
 }
 
-/// Build an `FBig` from an f64 with an explicit precision context.
+/// Build a `Big` from an f64 with an explicit precision.
 pub fn big_from_f64(x: f64, bits: usize) -> Big {
-    Big::try_from(x)
+    Big::from_f64(x, bits)
-        .unwrap_or_default()
+}
-        .with_precision(bits)
+
-        .value()
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn sc(x: f64) -> Scale {
+        Scale::from_f64(x)
+    }
+
+    fn re_im_f64(v: &ViewState) -> (f64, f64) {
+        let re: f64 = v.center_re.to_f64();
+        let im: f64 = v.center_im.to_f64();
+        (re, im)
+    }
+
+    #[test]
+    fn interpolate_view_hits_exact_endpoints() {
+        let bits = precision_for(sc(1.0));
+        let from =
+            ViewState::with_center(big_from_f64(-0.5, bits), big_from_f64(0.0, bits), sc(1.5));
+        let to = ViewState::with_center(
+            big_from_f64(-0.7515, precision_for(sc(1e-20))),
+            big_from_f64(0.1013, precision_for(sc(1e-20))),
+            sc(1e-20),
+        );
+
+        let start = interpolate_view(&from, &to, 0.0);
+        assert_eq!(re_im_f64(&start), re_im_f64(&from));
+        assert_eq!(start.half_height, from.half_height);
+
+        let end = interpolate_view(&from, &to, 1.0);
+        assert_eq!(re_im_f64(&end), re_im_f64(&to));
+        assert_eq!(end.half_height, to.half_height);
+    }
+
+    /// Regression test: a deep zoom's center used to be blended linearly in
+    /// `t` while `half_height` shrank geometrically, so partway through the
+    /// animation the offset from the target would already be far larger than
+    /// the (tiny, geometrically-shrunk) view — the target only snapped into
+    /// frame on the very last frame. The offset/half_height ratio should
+    /// instead stay roughly bounded throughout.
+    #[test]
+    fn interpolate_view_keeps_target_offset_bounded() {
+        let bits = precision_for(sc(1.0));
+        let from =
+            ViewState::with_center(big_from_f64(-0.5, bits), big_from_f64(0.0, bits), sc(1.5));
+        let to = ViewState::with_center(
+            big_from_f64(-0.7515, precision_for(sc(1e-20))),
+            big_from_f64(0.1013, precision_for(sc(1e-20))),
+            sc(1e-20),
+        );
+        let (to_re, to_im) = re_im_f64(&to);
+
+        for i in 1..10 {
+            let t = i as f64 / 10.0;
+            let mid = interpolate_view(&from, &to, t);
+            let (re, im) = re_im_f64(&mid);
+            let offset = ((re - to_re).powi(2) + (im - to_im).powi(2)).sqrt();
+            let ratio = offset / mid.half_height.to_f64();
+            assert!(
+                ratio < 10.0,
+                "t={t}: offset/half_height ratio {ratio} blew up (offset={offset}, half_height={})",
+                mid.half_height
+            );
+        }
+    }
+
+    #[test]
+    fn scale_parse_display_round_trip() {
+        for s in [
+            "1.25",
+            "1e-20",
+            "1.5e-20",
+            "3.7e-4000",
+            "1e-400",
+            "9.99999e-310",
+        ] {
+            let a: Scale = s.parse().unwrap();
+            let b: Scale = a.to_string().parse().unwrap();
+            assert_eq!(a, b, "{s} -> {a}");
+        }
+        assert_eq!("1.25".parse::<Scale>().unwrap().to_f64(), 1.25);
+        assert_eq!(sc(1.5e-20).to_string(), "1.5e-20");
+        let deep: Scale = "3.7e-4000".parse().unwrap();
+        assert_eq!(deep.to_string(), "3.7e-4000");
+        assert_eq!(format!("{deep:.2}"), "3.70e-4000");
+        assert!((deep.log10() - (3.7f64.log10() - 4000.0)).abs() < 1e-9);
+        assert!("0".parse::<Scale>().is_err());
+        assert!("-1e-500".parse::<Scale>().is_err());
+        assert!("abc".parse::<Scale>().is_err());
+    }
+
+    #[test]
+    fn scale_arithmetic() {
+        let a: Scale = "1e-1000".parse().unwrap();
+        let b = a.mul_f64(0.25);
+        assert!((b.ratio(a) - 0.25).abs() < 1e-15);
+        assert!(b < a && a > b);
+        assert_eq!(a.mul_f64(3.0).mul_f64(1.0 / 3.0).exponent(), a.exponent());
+        assert_eq!(sc(1.0).exponent(), 0);
+        assert_eq!(sc(0.75).exponent(), -1);
+        assert_eq!(sc(4.0).scaled_f64(-2), 1.0);
+        assert_eq!(
+            a.scaled_f64(-a.exponent()),
+            a.mul_f64(1.0).scaled_f64(-a.exponent())
+        );
+        assert!((1.0..2.0).contains(&a.scaled_f64(-a.exponent())));
+        assert_eq!(a.to_f64(), 0.0);
+        assert_eq!(Scale::MIN.mul_f64(0.5), Scale::MIN);
+        let p = precision_for(a);
+        assert!((3322 + 48..=3323 + 48).contains(&p), "{p}");
+    }
+
+    /// Past f64's range, the center must still land on the target at the
+    /// same geometric pace as the half-height.
+    #[test]
+    fn interpolate_view_past_f64_range() {
+        let from = ViewState::with_center(big_from_f64(-0.5, 64), big_from_f64(0.0, 64), sc(1.5));
+        let hh: Scale = "1e-1000".parse().unwrap();
+        let bits = precision_for(hh);
+        let to =
+            ViewState::with_center(big_from_f64(-0.7515, bits), big_from_f64(0.1013, bits), hh);
+        let end = interpolate_view(&from, &to, 1.0);
+        assert_eq!(end.half_height, hh);
+        assert_eq!(re_im_f64(&end), re_im_f64(&to));
+        let mut prev = from.half_height;
+        for i in 1..20 {
+            let t = i as f64 / 20.0;
+            let mid = interpolate_view(&from, &to, t);
+            assert!(mid.half_height < prev);
+            prev = mid.half_height;
+            // Offset from the target, in units of the view's half-height.
+            let k = -mid.half_height.exponent() as isize;
+            let dre = ((&mid.center_re - &to.center_re) << k).to_f64();
+            let dim = ((&mid.center_im - &to.center_im) << k).to_f64();
+            let ratio = (dre * dre + dim * dim).sqrt() / mid.half_height.scaled_f64(k as i32);
+            assert!(ratio > 0.01 && ratio < 10.0, "t={t}: ratio {ratio}");
+        }
+    }
 }

src/worker.rs

@@ -1,7 +1,7 @@
 //! Native background worker for reference-orbit computation.
 //!
 //! At deep zoom the high-precision reference can take many milliseconds (tens of
-//! thousands of `FBig` iterations), which would stutter the UI if done inline.
+//! thousands of `Big` iterations), which would stutter the UI if done inline.
 //! This runs it on a thread and coalesces bursts of requests (e.g. during a
 //! drag) down to the most recent one. On the web we compute inline instead
 //! (browsers need a Web Worker for threads); see `app.rs`.
@@ -9,26 +9,38 @@
 use std::sync::mpsc::{Receiver, Sender, TryRecvError, channel};
 use std::thread;
 
-use crate::fractal::{FractalKind, compute_reference, compute_set_reference};
+use crate::fractal::{FractalKind, RefOrbit, compute_reference, compute_set_reference};
-use crate::view::{Big, big_from_f64};
+use crate::view::{Big, Scale, big_from_f64};
 
 pub struct RefRequest {
     pub center_re: Big,
     pub center_im: Big,
-    pub half_height: f64,
+    pub half_height: Scale,
     pub julia: bool,
     pub julia_c: (f64, f64),
     pub max_iter: u32,
     pub precision: usize,
     pub kind: FractalKind,
     pub power: u32,
+    /// Distortion constant for the Phoenix map (ignored by other kinds).
+    pub phoenix_p: (f64, f64),
+    /// Distortion constant for the Lambda map (ignored by other kinds).
+    pub lambda_l: (f64, f64),
+    /// Complex exponent for the Complex Multibrot kind (ignored by other kinds).
+    pub complex_power: (f64, f64),
+    /// Kind-switch morph: `(from_kind, weight)` blended into every step.
+    pub morph: Option<(FractalKind, f32)>,
 }
 
 pub struct RefResult {
     pub center_re: Big,
     pub center_im: Big,
-    pub half_height: f64,
+    pub half_height: Scale,
-    pub points: Vec<[f32; 2]>,
+    pub points: RefOrbit,
+    /// The kind and morph `points` was computed with (echoed from the
+    /// request).
+    pub kind: FractalKind,
+    pub morph: Option<(FractalKind, f32)>,
 }
 
 pub struct RefWorker {
@@ -62,6 +74,8 @@ impl RefWorker {
                             center_im: req.center_im,
                             half_height: req.half_height,
                             points,
+                            kind: req.kind,
+                            morph: req.morph,
                         })
                         .is_err()
                     {
@@ -88,7 +102,7 @@ impl RefWorker {
     }
 }
 
-fn compute(req: &RefRequest) -> Vec<[f32; 2]> {
+fn compute(req: &RefRequest) -> RefOrbit {
     if req.julia {
         let jr = big_from_f64(req.julia_c.0, req.precision);
         let ji = big_from_f64(req.julia_c.1, req.precision);
@@ -101,6 +115,10 @@ fn compute(req: &RefRequest) -> Vec<[f32; 2]> {
             req.precision,
             req.kind,
             req.power,
+            req.phoenix_p,
+            req.lambda_l,
+            req.complex_power,
+            req.morph.map(|(k, w)| (k, w as f64)),
         )
     } else {
         compute_set_reference(
@@ -110,6 +128,10 @@ fn compute(req: &RefRequest) -> Vec<[f32; 2]> {
             req.precision,
             req.kind,
             req.power,
+            req.phoenix_p,
+            req.lambda_l,
+            req.complex_power,
+            req.morph.map(|(k, w)| (k, w as f64)),
         )
     }
 }

tests/shader_valid.rs

@@ -3,7 +3,7 @@
 //! shader with the same `naga` version wgpu uses — catching shader errors
 //! without needing a GPU or a display.
 
-fn validate(name: &str, src: &str) {
+fn validate(name: &str, src: &str) -> (naga::Module, naga::valid::ModuleInfo) {
     let module = match naga::front::wgsl::parse_str(src) {
         Ok(m) => m,
         Err(e) => panic!("{name}: WGSL parse error:\n{}", e.emit_to_string(src)),
@@ -12,20 +12,160 @@ fn validate(name: &str, src: &str) {
         naga::valid::ValidationFlags::all(),
         naga::valid::Capabilities::all(),
     );
-    if let Err(e) = validator.validate(&module) {
+    match validator.validate(&module) {
-        panic!("{name}: WGSL validation error:\n{}", e.emit_to_string(src));
+        Ok(info) => (module, info),
+        Err(e) => panic!("{name}: WGSL validation error:\n{}", e.emit_to_string(src)),
+    }
+}
+
+/// Number of fractal kinds, i.e. the `const KIND_*` declarations in
+/// common.wgsl (one per `FractalKind` variant, values 0..N).
+fn kind_count() -> u32 {
+    let n = include_str!("../src/shaders/common.wgsl")
+        .lines()
+        .filter(|l| l.starts_with("const KIND_"))
+        .count() as u32;
+    assert!(n >= 10, "found only {n} KIND_* constants in common.wgsl");
+    n
+}
+
+/// Specialize `module`'s `override`s with `constants` for `entry_point` (as
+/// wgpu does at pipeline creation) and compile the result to SPIR-V, so a
+/// shader that only breaks once a particular override value folds a branch
+/// in or out is still caught.
+fn specialize(
+    name: &str,
+    module: &naga::Module,
+    info: &naga::valid::ModuleInfo,
+    stage: naga::ShaderStage,
+    entry_point: &str,
+    constants: &[(&str, f64)],
+) {
+    let mut pc = naga::back::PipelineConstants::default();
+    for (k, v) in constants {
+        pc.insert((*k).to_string(), *v);
+    }
+    let (module, info) = naga::back::pipeline_constants::process_overrides(
+        module,
+        info,
+        Some((stage, entry_point)),
+        &pc,
+    )
+    .unwrap_or_else(|e| panic!("{name} {entry_point} {constants:?}: override error: {e:?}"));
+    let pipeline = naga::back::spv::PipelineOptions {
+        shader_stage: stage,
+        entry_point: entry_point.to_string(),
+    };
+    naga::back::spv::write_vec(
+        &module,
+        &info,
+        &naga::back::spv::Options::default(),
+        Some(&pipeline),
+    )
+    .unwrap_or_else(|e| panic!("{name} {entry_point} {constants:?}: SPIR-V error: {e:?}"));
+}
+
+const MANDELBROT_SRC: &str = concat!(
+    include_str!("../src/shaders/common.wgsl"),
+    include_str!("../src/shaders/iterate_uniforms.wgsl"),
+    include_str!("../src/shaders/mandelbrot.wgsl"),
+);
+
+#[test]
+fn mandelbrot_shader_is_valid() {
+    validate("mandelbrot.wgsl", MANDELBROT_SRC);
+}
+
+/// Every specialization renderer.rs can build (`PipelineKey`: kind × Julia ×
+/// DE × morph × deep), for every fragment entry point.
+#[test]
+fn mandelbrot_shader_specializations_compile() {
+    let (module, info) = validate("mandelbrot.wgsl", MANDELBROT_SRC);
+    for kind in 0..kind_count() {
+        for julia in [0.0, 1.0] {
+            for de in [0.0, 1.0] {
+                for morph in [0.0, 1.0] {
+                    for deep in [0.0, 1.0] {
+                        let constants = [
+                            ("KIND", kind as f64),
+                            ("IS_JULIA", julia),
+                            ("DE", de),
+                            ("MORPH", morph),
+                            ("DEEP", deep),
+                        ];
+                        for entry in ["fs_data", "fs_refine", "fs_color"] {
+                            specialize(
+                                "mandelbrot.wgsl",
+                                &module,
+                                &info,
+                                naga::ShaderStage::Fragment,
+                                entry,
+                                &constants,
+                            );
+                        }
+                    }
+                }
+            }
+        }
     }
 }
 
 #[test]
-fn mandelbrot_shader_is_valid() {
+fn colorize_shader_is_valid() {
     validate(
-        "mandelbrot.wgsl",
+        "colorize.wgsl",
-        include_str!("../src/shaders/mandelbrot.wgsl"),
+        concat!(
+            include_str!("../src/shaders/common.wgsl"),
+            include_str!("../src/shaders/iterate_uniforms.wgsl"),
+            include_str!("../src/shaders/colorize.wgsl"),
+        ),
+    );
+}
+
+#[test]
+fn lipschitz_shader_is_valid() {
+    validate(
+        "lipschitz.wgsl",
+        concat!(
+            include_str!("../src/shaders/common.wgsl"),
+            include_str!("../src/shaders/lipschitz.wgsl"),
+        ),
     );
 }
 
 #[test]
 fn blit_shader_is_valid() {
-    validate("blit.wgsl", include_str!("../src/shaders/blit.wgsl"));
+    validate(
+        "blit.wgsl",
+        concat!(
+            include_str!("../src/shaders/common.wgsl"),
+            include_str!("../src/shaders/blit.wgsl"),
+        ),
+    );
+}
+
+const BUDDHABROT_SRC: &str = concat!(
+    include_str!("../src/shaders/common.wgsl"),
+    include_str!("../src/shaders/buddhabrot.wgsl"),
+);
+
+#[test]
+fn buddhabrot_shader_is_valid() {
+    validate("buddhabrot.wgsl", BUDDHABROT_SRC);
+}
+
+/// Every per-kind accumulation pipeline buddhabrot.rs can build.
+#[test]
+fn buddhabrot_shader_specializations_compile() {
+    let (module, info) = validate("buddhabrot.wgsl", BUDDHABROT_SRC);
+    for kind in 0..kind_count() {
+        specialize(
+            "buddhabrot.wgsl",
+            &module,
+            &info,
+            naga::ShaderStage::Compute,
+            "cs_main",
+            &[("KIND", kind as f64)],
+        );
+    }
 }

tools/bench/.gitignore

@@ -0,0 +1,2 @@
+results/
+.worktrees/

tools/bench/README.md

@@ -0,0 +1,48 @@
+# Benchmarks
+
+`bench.sh` times `mandelbrot --headless` on a fixed set of views with
+[hyperfine](https://github.com/sharkdp/hyperfine). That's the whole real
+pipeline: the reference orbit on the CPU, then the GPU render, readback and PNG
+encode. It builds the headless-only binary (`--no-default-features`) itself.
+
+```sh
+tools/bench/bench.sh --rev HEAD            # did my uncommitted edits help? (vs last commit)
+tools/bench/bench.sh --rev main seahorse-1e300   # one scenario vs another branch
+tools/bench/bench.sh --quick               # all scenarios, 960×540, 3 runs
+tools/bench/bench.sh                       # all scenarios, 1920×1080, 5 runs
+tools/bench/bench.sh --list
+```
+
+`--rev REF` checks REF out into `.worktrees/<sha>` and builds it there, with its
+own target dir, so your `target/` stays warm. Each scenario then runs both
+binaries back to back in one hyperfine call. The line to read is
+`working tree ran 1.23 ± 0.04 times faster than main (…)`. A ratio within about
+2σ of 1.00 is noise.
+
+Results (hyperfine JSON and markdown per scenario) go to
+`results/<sha>[-dirty]/`, or `results/<rev>-vs-<sha>/` with `--rev`.
+Both `results/` and `.worktrees/` are git-ignored. To clean up:
+`rm -rf tools/bench/.worktrees && git worktree prune`.
+
+## Scenarios
+
+| name | mostly measures |
+|---|---|
+| `shallow` | GPU, plain f32 path, f64 orbit fast path |
+| `seahorse-1e30` | GPU f32 perturbation from a `Big` orbit |
+| `seahorse-1e100` | the `DEEP` shader pipeline |
+| `elephant-1e100-aa-de` | 2×2 antialiasing + DE shading |
+| `burning-ship` | a non-holomorphic kind |
+| `3d` | the raymarched 3D export path |
+| `anim-zoom` | 24-frame zoom (⅓ size): the parallel orbit, GPU and PNG pipeline |
+| `seahorse-1e300` *(slow)* | ~270k iterations per pixel on the deep path, ~40 s per run even with `--quick`. It's GPU-bound: the orbit itself is under a second. Only runs when named or with `--all` |
+
+Views come from `tools/deep-zoom/LOCATIONS.md`. Each wall time includes process
+start, device creation and shader compilation, so a small change to a GPU-bound
+scenario shows up diluted.
+
+## Tips
+
+- Keep the machine idle and on AC power. Other GPU apps (browsers, video) add a lot of noise.
+- Use `--quick` while you iterate and a full run to confirm.
+- Timings are only comparable on the same machine and GPU.

tools/bench/bench.sh

@@ -0,0 +1,128 @@
+#!/usr/bin/env bash
+# Benchmark `mandelbrot --headless` on a fixed set of scenarios with hyperfine.
+#
+# Usage:
+#   bench.sh [--quick] [--runs N] [--rev REF] [--all] [--list] [scenario...]
+#
+#   (default)   time the working tree; results go to results/<sha>[-dirty]/
+#   --rev REF   also build REF (in a git worktree) and time both binaries side
+#               by side; hyperfine prints "X ± σ times faster" per scenario
+#   --quick     960×540 and 3 runs instead of 1920×1080 and 5
+#   --runs N    timed runs per command (after 1 warmup run)
+#   --all       include the slow scenarios
+#   --list      print the scenario names and exit
+#
+# With no scenario names, all but the slow ones run. See README.md.
+
+set -euo pipefail
+
+here=$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)
+root=$(git -C "$here" rev-parse --show-toplevel)
+
+# Views from tools/deep-zoom/LOCATIONS.md.
+SEAHORSE_40='-0.77568376800905379745347652613832924487504096622022,0.13646736829469012473375311880735014411233827361594'
+SEAHORSE_101='-0.77568376800905379746948350393474104572824650461579342765769586746577714101553375163935420167637213972439444483,0.13646736829469012473327440961784876519777211159246218448277041663416833530840062457397927487282583495378053495'
+SEAHORSE_300='-0.775683768009053797469483503934741045728246504615800394794952001400666017222819589894883159368782255028252296689050972508942991790804637379375064948276511044167168394677127466362472192356953918438738697548775738756167744421444715134058363508346750264411321139485834882343906172015818621107808449401958194265462,0.136467368294690124733274409617848765197772111592467696407800195400835665974815500875448611244178656625706823059759836009902469392551108149827753781145338163746214967880988693412636771323356061132825037923307975359146666033691080243216637006179374407866237575096209504710178751614036006531433101633993532313930'
+ELEPHANT_100='0.2920738619144539179997175176922057340804018914331633820622644536373359023331882946705674169275530423410817910,0.01577091721139011808246902823033833768260048863232968822435568049949556139801802963232184866659058960379114747'
+
+# name -> headless args (no size or --export-path; those are added per run).
+# Order matters for display, hence the separate list. SLOW ones (tens of
+# seconds per run) only run when named or with --all.
+SCENARIOS=(shallow seahorse-1e30 seahorse-1e100 elephant-1e100-aa-de burning-ship 3d anim-zoom)
+SLOW=(seahorse-1e300)
+declare -A ARGS=(
+    [shallow]="--view=-0.75,0,1.5"
+    [seahorse-1e30]="--view=$SEAHORSE_40,1e-30"
+    [seahorse-1e100]="--view=$SEAHORSE_101,3.4e-101"
+    [seahorse-1e300]="--view=$SEAHORSE_300,5.5e-300"
+    [elephant-1e100-aa-de]="--view=$ELEPHANT_100,1e-75 --antialias --de"
+    [burning-ship]="--kind burning-ship"
+    [3d]="--rendering-kind 3d --de --pitch -40 --view=-0.75,0,1.5"
+    [anim-zoom]="--view=-0.75,0,1.5 --to-view=$SEAHORSE_40,1e-30 --frames 24"
+)
+
+quick=0
+runs=
+rev=
+picked=()
+while (($#)); do
+    case $1 in
+        --quick) quick=1 ;;
+        --runs) runs=$2; shift ;;
+        --rev) rev=$2; shift ;;
+        --all) picked+=("${SCENARIOS[@]}" "${SLOW[@]}") ;;
+        --list) printf '%s\n' "${SCENARIOS[@]}"; printf '%s (slow)\n' "${SLOW[@]}"; exit 0 ;;
+        -h|--help) sed -n '2,16s/^# \{0,1\}//p' "$0"; exit 0 ;;
+        -*) echo "unknown option: $1" >&2; exit 2 ;;
+        *)
+            [[ -v ARGS[$1] ]] || { echo "unknown scenario: $1 (try --list)" >&2; exit 2; }
+            picked+=("$1") ;;
+    esac
+    shift
+done
+((${#picked[@]})) || picked=("${SCENARIOS[@]}")
+
+if ((quick)); then
+    width=960 height=540 runs=${runs:-3}
+else
+    width=1920 height=1080 runs=${runs:-5}
+fi
+
+command -v hyperfine >/dev/null || { echo "hyperfine not found (https://github.com/sharkdp/hyperfine)" >&2; exit 1; }
+
+# Headless-only binary: no eframe/egui, faster to build, same render path.
+build() { cargo build --release --no-default-features --quiet --manifest-path "$1/Cargo.toml"; }
+
+echo "building working tree…" >&2
+build "$root"
+new_bin="$root/target/release/mandelbrot"
+
+if [[ -n $rev ]]; then
+    rev_sha=$(git -C "$root" rev-parse --short "$rev^{commit}")
+    wt="$here/.worktrees/$rev_sha"
+    [[ -d $wt ]] || git -C "$root" worktree add --detach --quiet "$wt" "$rev_sha"
+    echo "building $rev ($rev_sha)…" >&2
+    # Separate target dir so switching revisions doesn't invalidate target/.
+    CARGO_TARGET_DIR="$here/.worktrees/target" build "$wt"
+    old_bin="$here/.worktrees/target/release/mandelbrot"
+fi
+
+tmp=$(mktemp -d)
+trap 'rm -rf "$tmp"' EXIT
+
+sha=$(git -C "$root" rev-parse --short HEAD)
+git -C "$root" diff --quiet HEAD -- . ':!tools/bench' || sha+=-dirty
+out="$here/results/${rev:+$rev_sha-vs-}$sha"
+mkdir -p "$out"
+
+# Full headless command line for scenario $2 with binary $1.
+command_for() {
+    local bin=$1 name=$2 w=$width h=$height dest=$tmp/$2.png
+    if [[ $name == anim-* ]]; then
+        # Animation: a directory of frames, at a smaller size.
+        w=$((width / 3)) h=$((height / 3)) dest=$tmp/$name
+    fi
+    echo "$bin --headless --width $w --height $h --export-path $dest ${ARGS[$name]}"
+}
+
+for name in "${picked[@]}"; do
+    echo >&2
+    echo "=== $name ===" >&2
+    if [[ -n $rev ]]; then
+        cmds=(-n "$rev ($rev_sha)" "$(command_for "$old_bin" "$name")"
+              -n "working tree" "$(command_for "$new_bin" "$name")")
+    else
+        cmds=(-n "$name" "$(command_for "$new_bin" "$name")")
+    fi
+    hyperfine --warmup 1 --runs "$runs" --style basic \
+        --export-json "$out/$name.json" --export-markdown "$out/$name.md" \
+        "${cmds[@]}"
+done
+
+echo
+echo "## Summary (${width}×${height}, $runs runs; results in ${out#"$root"/}/)"
+for name in "${picked[@]}"; do
+    echo
+    echo "### $name"
+    cat "$out/$name.md"
+done

tools/deep-zoom/LOCATIONS.md

@@ -0,0 +1,167 @@
+# Deep-zoom locations
+
+Beautiful deep Mandelbrot locations, all computed with `find_deep.py` and checked with a
+`--headless` render. Every one is an exact minibrot nucleus (Newton's method at
+`2·depth + 60` digits), not a coordinate copied from somewhere, so the digits are right all
+the way down.
+
+## How to use them
+
+Each location has two views on the same centre:
+
+- **Minibrot:** half-height ≈ 3× the minibrot's size. A tiny copy of the whole set sits in
+  concentric colour bands, and there are more bands the deeper it is.
+- **Embedded Julia set:** half-height ≈ size^0.75, about ¾ of the way down in log-zoom.
+  This is where each location looks unique. The minibrots all look alike.
+
+```sh
+cargo run --release -- --view=RE,IM,HALF_HEIGHT        # interactive
+cargo run --release -- --headless --view=RE,IM,HALF_HEIGHT --export-path shot.png
+# zoom video from the full set down to a minibrot, piped to ffmpeg (see Makefile):
+cargo run --release -- --headless --view=-0.75,0,1.5 --to-view=RE,IM,HALF_HEIGHT \
+    --fps 60 --duration 60 --export-path - | make hevc-nvenc
+```
+
+Pass negative coordinates as `--view=-0.77...` (with the `=`): clap would read `--view -0.77...` as a flag.
+Iterations scale with depth automatically (about 90k at 10⁻¹⁰⁰ and 270k at 10⁻³⁰⁰), which is
+enough for these periods.
+
+## Infinite spirals (Misiurewicz points)
+
+These are the anchor points. Zoom straight into one and the same spiral repeats forever,
+at any depth. Every minibrot below sits just beside one of them.
+
+| Region | Point | Preperiod, period | Looks like |
+|---|---|---|---|
+| Seahorse valley | `-0.7756837680090537974694835039347410457282465046158` `0.13646736829469012473327440961784876519777211159247` | 24, 2 | Two-armed spirals of seahorses, repeating at every depth. |
+| Elephant valley | `0.29207386191445391799971751769220573408040189143315` `0.015770917211390118082469028230338337682600488632339` | 32, 3 | Three-armed spirals of elephant trunks. |
+| Top antenna | `-0.10110375797210418675706890936004723524958119917843` `0.95629400795235409290719434118824484558046591980423` | 38, 4 | Four-armed branch points on the upper antenna, with thin dendrites instead of spirals. |
+
+## Seahorse valley
+
+### Seahorse valley, minibrot at 3.7e-41 (period 1034)
+
+The embedded Julia set is a pale double spiral: two S-shaped arms of tiny seahorses wind into a bright centre, with a third lace band sweeping around them. The best one for a short video, and it renders in seconds.
+
+```sh
+# embedded Julia set
+--view=-0.77568376800905379745347652613832924487504096622022,0.13646736829469012473375311880735014411233827361594,1e-30
+# minibrot
+--view=-0.77568376800905379745347652613832924487504096622022,0.13646736829469012473375311880735014411233827361594,1.1e-40
+```
+
+### Seahorse valley, minibrot at 1.14e-101 (period 2868)
+
+At the Julia depth there's a dark blue field with a glowing core and lace threads crossing it.
+
+```sh
+# embedded Julia set
+--view=-0.77568376800905379746948350393474104572824650461579342765769586746577714101553375163935420167637213972439444483,0.13646736829469012473327440961784876519777211159246218448277041663416833530840062457397927487282583495378053495,1e-76
+# minibrot
+--view=-0.77568376800905379746948350393474104572824650461579342765769586746577714101553375163935420167637213972439444483,0.13646736829469012473327440961784876519777211159246218448277041663416833530840062457397927487282583495378053495,3.4e-101
+```
+
+### Seahorse valley, minibrot at 1.37e-200 (period 5895)
+
+Two filaments cross in an X over a warm brown background, with a small dark spiral where they meet.
+
+```sh
+# embedded Julia set
+--view=-0.77568376800905379746948350393474104572824650461580039479495200140066601722281958989488315936878225494657853849784368247991666558116221905228489656259693587754973261632614186930985854124920967267440737850057557,0.13646736829469012473327440961784876519777211159246769640780019540083566597481550087544861124417865661202932094564677695883049019713653069907950852152823160218141353878979871215911794286224832089496659451498185,1e-150
+# minibrot
+--view=-0.77568376800905379746948350393474104572824650461580039479495200140066601722281958989488315936878225494657853849784368247991666558116221905228489656259693587754973261632614186930985854124920967267440737850057557,0.13646736829469012473327440961784876519777211159246769640780019540083566597481550087544861124417865661202932094564677695883049019713653069907950852152823160218141353878979871215911794286224832089496659451498185,4.1e-200
+```
+
+### Seahorse valley, minibrot at 1.83e-300 (period 8922)
+
+Faint cream threads, and a spiral wound so tight it reads as a point. Period 8922, so the minibrot needs a long render.
+
+```sh
+# embedded Julia set
+--view=-0.775683768009053797469483503934741045728246504615800394794952001400666017222819589894883159368782255028252296689050972508942991790804637379375064948276511044167168394677127466362472192356953918438738697548775738756167744421444715134058363508346750264411321139485834882343906172015818621107808449401958194265462,0.136467368294690124733274409617848765197772111592467696407800195400835665974815500875448611244178656625706823059759836009902469392551108149827753781145338163746214967880988693412636771323356061132825037923307975359146666033691080243216637006179374407866237575096209504710178751614036006531433101633993532313930,1e-225
+# minibrot
+--view=-0.775683768009053797469483503934741045728246504615800394794952001400666017222819589894883159368782255028252296689050972508942991790804637379375064948276511044167168394677127466362472192356953918438738697548775738756167744421444715134058363508346750264411321139485834882343906172015818621107808449401958194265462,0.136467368294690124733274409617848765197772111592467696407800195400835665974815500875448611244178656625706823059759836009902469392551108149827753781145338163746214967880988693412636771323356061132825037923307975359146666033691080243216637006179374407866237575096209504710178751614036006531433101633993532313930,5.5e-300
+```
+
+## Elephant valley
+
+### Elephant valley, minibrot at 1.29e-100 (period 782)
+
+A cream-coloured double S-spiral, like the seahorse one but with fatter, beaded arms.
+
+```sh
+# embedded Julia set
+--view=0.2920738619144539179997175176922057340804018914331633820622644536373359023331882946705674169275530423410817910,0.01577091721139011808246902823033833768260048863232968822435568049949556139801802963232184866659058960379114747,1e-75
+# minibrot
+--view=0.2920738619144539179997175176922057340804018914331633820622644536373359023331882946705674169275530423410817910,0.01577091721139011808246902823033833768260048863232968822435568049949556139801802963232184866659058960379114747,3.9e-100
+```
+
+### Elephant valley, minibrot at 1.43e-199 (period 1585)
+
+A single huge spiral arm made of blue beads curling across the whole frame.
+
+```sh
+# embedded Julia set
+--view=0.2920738619144539179997175176922057340804018914331538397786950546981063169810374784665382516408545756138262706218874924432355556243165250541700374639889797148498919340003273815669351046658761147565052417000965,0.01577091721139011808246902823033833768260048863233880759961760295375606839216565332458201188913912642954367433579737643167232896069795830226759356080847862646789481028238105648099709502522309228500630759855757,1e-149
+# minibrot
+--view=0.2920738619144539179997175176922057340804018914331538397786950546981063169810374784665382516408545756138262706218874924432355556243165250541700374639889797148498919340003273815669351046658761147565052417000965,0.01577091721139011808246902823033833768260048863233880759961760295375606839216565332458201188913912642954367433579737643167232896069795830226759356080847862646789481028238105648099709502522309228500630759855757,4.3e-199
+```
+
+### Elephant valley, minibrot at 3.82e-300 (period 2395)
+
+A spiral galaxy: several beaded arms around a pinwheel centre. One of the prettiest frames here.
+
+```sh
+# embedded Julia set
+--view=0.292073861914453917999717517692205734080401891433153839778695054698106316981037478466538251640854575589843066619974864800862332115945960921998657430606126553202998390050225413256445451049563878137878839982267258218894836912449161037745627504826537881261626243871678392881757578278459983842286413975991353319739,0.0157709172113901180824690282303383376826004886323388075996176029537560683921656533245820118891391263013273917522825544701901299061542128984468742890308365571942081484001405437827548345359998503228665872823816067983725089244499770271352539008763406229496083105636482420467114597267096082878888045800333807911146,1e-225
+# minibrot
+--view=0.292073861914453917999717517692205734080401891433153839778695054698106316981037478466538251640854575589843066619974864800862332115945960921998657430606126553202998390050225413256445451049563878137878839982267258218894836912449161037745627504826537881261626243871678392881757578278459983842286413975991353319739,0.0157709172113901180824690282303383376826004886323388075996176029537560683921656533245820118891391263013273917522825544701901299061542128984468742890308365571942081484001405437827548345359998503228665872823816067983725089244499770271352539008763406229496083105636482420467114597267096082878888045800333807911146,1.1e-299
+```
+
+## Top antenna
+
+### Top antenna, minibrot at 6.11e-101 (period 245)
+
+A dark branching dendrite like a frost cross, with four-way junctions.
+
+```sh
+# embedded Julia set
+--view=-0.10110375797210418675706890936004723524958119917842627217950669362738928440088634862532432662296073501093701563,0.95629400795235409290719434118824484558046591980423293884325556254155313535666457147658005358708674409029391915,1e-75
+# minibrot
+--view=-0.10110375797210418675706890936004723524958119917842627217950669362738928440088634862532432662296073501093701563,0.95629400795235409290719434118824484558046591980423293884325556254155313535666457147658005358708674409029391915,1.8e-100
+```
+
+### Top antenna, minibrot at 5.28e-200 (period 473)
+
+A chain of six-armed snowflakes linked by thin filaments.
+
+```sh
+# embedded Julia set
+--view=-0.10110375797210418675706890936004723524958119917842839398761868801597328463328677019373309617158827470368429189213012997868613724029746440432852247903869013157556141380437202406412221853553594880182186959159214,0.95629400795235409290719434118824484558046591980423399388630140415938010604675760901574969597486831722998038561988250849596064882005832681021199867736493316924923123916964900533995659228499205141785254396348248,1e-149
+# minibrot
+--view=-0.10110375797210418675706890936004723524958119917842839398761868801597328463328677019373309617158827470368429189213012997868613724029746440432852247903869013157556141380437202406412221853553594880182186959159214,0.95629400795235409290719434118824484558046591980423399388630140415938010604675760901574969597486831722998038561988250849596064882005832681021199867736493316924923123916964900533995659228499205141785254396348248,1.6e-199
+```
+
+### Top antenna, minibrot at 8.34e-301 (period 705)
+
+A single twelve-armed star, very symmetric. The antenna minibrots have short periods (245-705), so these are the fastest deep renders.
+
+```sh
+# embedded Julia set
+--view=-0.1011037579721041867570689093600472352495811991784283939876186880159732846332867701937330961715882746718394428627914481009391257007785408536971203165750666758077852384490279260184029373211737264310068845597273991782305778295187471341711226626762421910644338164121042775094463557363347706110614218633830535086184,0.9562940079523540929071943411882448455804659198042339938863014041593801060467576090157496959748683171680339080646917869452781885502668216669916185990922330667568398963038228431738928191227884090004548615469303071899797403388188723954061899156655653387543351937028936674153437083087070219108726088551230849901498,1e-225
+# minibrot
+--view=-0.1011037579721041867570689093600472352495811991784283939876186880159732846332867701937330961715882746718394428627914481009391257007785408536971203165750666758077852384490279260184029373211737264310068845597273991782305778295187471341711226626762421910644338164121042775094463557363347706110614218633830535086184,0.9562940079523540929071943411882448455804659198042339938863014041593801060467576090157496959748683171680339080646917869452781885502668216669916185990922330667568398963038228431738928191227884090004548615469303071899797403388188723954061899156655653387543351937028936674153437083087070219108726088551230849901498,2.5e-300
+```
+
+## Finding more
+
+```sh
+./find_deep.py --list                  # known regions
+./find_deep.py seahorse 250            # minibrot of size ~1e-500 near the seahorse point
+./find_deep.py seahorse 100 0.2,0.7    # a different minibrot at the same depth
+./find_deep.py -0.1011,0.9563,38,4 80  # any Misiurewicz point, given as re,im,k,p
+```
+
+A disk of radius 10⁻ᴰ around a Misiurewicz point holds a minibrot of size about 10⁻²ᴰ.
+Newton sometimes fails to converge (elephant at depth 100 with the default offset did). The
+script detects this from the size and asks for a different offset. Needs `mpmath`.

tools/deep-zoom/find_deep.py

@@ -0,0 +1,145 @@
+#!/usr/bin/env python3
+"""Find deep Mandelbrot minibrots near a Misiurewicz point.
+
+Misiurewicz points (preperiodic c, f^(k+p)(0) = f^k(0)) have self-similar
+spirals at every depth. A disk of radius r = 10^-D around one contains a
+minibrot of size ~r^2, found by:
+
+  1. the ball-period method: the first n where the disk's image covers 0
+     gives the period p of a nucleus inside it;
+  2. Newton's method on f^p(0) = 0 at high precision for the nucleus;
+  3. the standard size estimate (Heiland-Allen) for its scale.
+
+Zooming at the nucleus shows spirals, then an embedded Julia set (around
+size^0.75), then the minibrot (half-height ~3x size).
+
+Usage:
+  find_deep.py REGION DEPTH [OFFSET_RE,OFFSET_IM]
+  find_deep.py --list
+
+REGION is a name from REGIONS or "re,im,k,p" for any Misiurewicz point.
+OFFSET (default 0.6,0.3, in units of r) picks a different minibrot at the
+same depth. If the printed size is far below 10^-(2*DEPTH), Newton didn't
+converge: try another offset.
+
+Needs mpmath (pip install mpmath).
+"""
+
+import sys
+
+from mpmath import log10, mp, mpc, mpf
+
+# name: (approximate seed, preperiod k, period p). The exact point is
+# refined by Newton at the requested precision.
+REGIONS = {
+    "seahorse": (("-0.77568377", "0.13646737"), 24, 2),
+    "elephant": (("0.2925", "0.0149"), 32, 3),
+    "antenna": (("-0.1011", "0.9563"), 38, 4),
+}
+
+
+def converged(d):
+    return abs(d) < mpf(10) ** (-mp.dps + 20)
+
+
+def misiurewicz(c, k, p, steps=200):
+    """Newton on f^(k+p)(0) - f^k(0) = 0."""
+    for _ in range(steps):
+        z = dz = mpc(0)
+        zk = dzk = None
+        for i in range(1, k + p + 1):
+            dz = 2 * z * dz + 1
+            z = z * z + c
+            if i == k:
+                zk, dzk = z, dz
+        d = (z - zk) / (dz - dzk)
+        c -= d
+        if converged(d):
+            break
+    return c
+
+
+def period_in_ball(c, r, maxit=1_000_000):
+    """First n where the disk of radius r around c maps onto a disk containing 0."""
+    z = dz = mpc(0)
+    for n in range(1, maxit):
+        dz = 2 * z * dz + 1
+        z = z * z + c
+        if abs(z) < abs(dz) * r:
+            return n
+        if abs(z) > 4:
+            return None
+    return None
+
+
+def nucleus(c, p, steps=200):
+    """Newton on f^p(0) = 0."""
+    for _ in range(steps):
+        z = dz = mpc(0)
+        for _ in range(p):
+            dz = 2 * z * dz + 1
+            z = z * z + c
+        d = z / dz
+        c -= d
+        if converged(d):
+            break
+    return c
+
+
+def size(c, p):
+    """Approximate size of the minibrot with nucleus c and period p."""
+    z = mpc(0)
+    l = b = mpc(1)
+    for _ in range(1, p):
+        z = z * z + c
+        l = 2 * z * l
+        b = b + 1 / l
+    return abs(1 / (b * l * l))
+
+
+def main(argv):
+    if len(argv) >= 1 and argv[0] == "--list":
+        for name, ((re, im), k, p) in REGIONS.items():
+            print(f"{name:10} ~{re}{'+' if not im.startswith('-') else ''}{im}i  M({k},{p})")
+        return 0
+    if len(argv) not in (2, 3):
+        print(__doc__, file=sys.stderr)
+        return 2
+
+    region, depth = argv[0], int(argv[1])
+    if region in REGIONS:
+        (re, im), k, p = REGIONS[region]
+    else:
+        re, im, k, p = region.split(",")
+        k, p = int(k), int(p)
+    off_re, off_im = argv[2].split(",") if len(argv) == 3 else ("0.6", "0.3")
+
+    mp.dps = 2 * depth + 60
+    m = misiurewicz(mpc(re, im), k, p)
+    r = mpf(10) ** (-depth)
+    c0 = m + r * mpc(off_re, off_im)
+    period = period_in_ball(c0, r)
+    if period is None:
+        print("no period found (the disk escapes)", file=sys.stderr)
+        return 1
+    n = nucleus(c0, period)
+    s = size(n, period)
+    if s < mpf(10) ** (-2 * depth - 10):
+        print(f"size {mp.nstr(s, 3)} is implausibly small: Newton didn't converge, "
+              "try another offset", file=sys.stderr)
+        return 1
+
+    digits = int(-log10(s)) + 10
+    log_s = float(log10(s))
+    re_s = mp.nstr(n.real, digits, strip_zeros=False)
+    im_s = mp.nstr(n.imag, digits, strip_zeros=False)
+    print(f"# {region} depth={depth} period={period} size={mp.nstr(s, 3)}")
+    print("# minibrot:")
+    print(f"--view={re_s},{im_s},{mp.nstr(3 * s, 2)}")
+    print(f"# embedded Julia set on the way down:")
+    print(f"--view={re_s},{im_s},1e{round(0.75 * log_s)}")
+    return 0
+
+
+if __name__ == "__main__":
+    sys.exit(main(sys.argv[1:]))

tools/encode/.gitignore

@@ -0,0 +1,3 @@
+clips/
+work/
+results/

tools/encode/configs/speed.txt

@@ -0,0 +1,8 @@
+# Pass 1: which presets fit the 3-5 fps budget at 4K on this machine.
+x265-fast      | -pix_fmt yuv420p10le -c:v libx265 -profile:v main10 -preset fast   -crf 18 -x265-params log-level=error:aq-mode=3:no-sao=1
+x265-medium    | -pix_fmt yuv420p10le -c:v libx265 -profile:v main10 -preset medium -crf 18 -x265-params log-level=error:aq-mode=3:no-sao=1
+x265-slow      | -pix_fmt yuv420p10le -c:v libx265 -profile:v main10 -preset slow   -crf 18 -x265-params log-level=error:aq-mode=3:no-sao=1
+av1-p5         | -pix_fmt yuv420p10le -c:v libsvtav1 -preset 5 -crf 26 -svtav1-params film-grain=0
+av1-p6         | -pix_fmt yuv420p10le -c:v libsvtav1 -preset 6 -crf 26 -svtav1-params film-grain=0
+av1-p7         | -pix_fmt yuv420p10le -c:v libsvtav1 -preset 7 -crf 26 -svtav1-params film-grain=0
+av1-p8         | -pix_fmt yuv420p10le -c:v libsvtav1 -preset 8 -crf 26 -svtav1-params film-grain=0

tools/encode/make_clips.sh

@@ -0,0 +1,66 @@
+#!/usr/bin/env bash
+# Render the lossless 4K60 test clips that sweep.sh encodes.
+#
+# Each clip goes through the same RGBA -> bt709 tv-range 10-bit conversion as
+# the Makefile, then into lossless FFV1. The clips are therefore exactly what the
+# encoders see, so VMAF against them measures the encoder alone.
+#
+#   tools/encode/make_clips.sh [--size WxH] [--seconds S] [--force] [clip...]
+set -euo pipefail
+
+here=$(cd "$(dirname "$0")" && pwd)
+root=$(cd "$here/../.." && pwd)
+out="$here/clips"
+size=3840x2160
+seconds=4
+fps=60
+force=0
+only=()
+
+while [[ $# -gt 0 ]]; do
+    case $1 in
+        --size) size=$2; shift 2 ;;
+        --seconds) seconds=$2; shift 2 ;;
+        --force) force=1; shift ;;
+        -h|--help) sed -n '2,9p' "$0"; exit 0 ;;
+        *) only+=("$1"); shift ;;
+    esac
+done
+
+# Seahorse valley, minibrot at 3.7e-41 (tools/deep-zoom/LOCATIONS.md).
+SH_RE=-0.77568376800905379745347652613832924487504096622022
+SH_IM=0.13646736829469012473375311880735014411233827361594
+
+# name | mandelbrot flags. Zoom speeds bracket a typical 60 s dive (~0.7 decade/s).
+clips=(
+    # Worst case: dense filaments, 1.5 decades/s of scaling motion.
+    "filaments|--view=$SH_RE,$SH_IM,1e-8 --to-view=$SH_RE,$SH_IM,3e-15 --linear"
+    # Smooth concentric bands closing in on the minibrot: banding/blocking risk.
+    "bands|--view=$SH_RE,$SH_IM,1e-38 --to-view=$SH_RE,$SH_IM,1.1e-40 --linear"
+    # Embedded Julia set, slow drift: fine static texture, psy/detail retention.
+    "julia|--view=$SH_RE,$SH_IM,2e-30 --to-view=$SH_RE,$SH_IM,1e-30 --linear"
+)
+
+[[ -x $root/target/release/mandelbrot ]] || cargo build --release --manifest-path "$root/Cargo.toml"
+mkdir -p "$out"
+w=${size%x*}
+h=${size#*x}
+
+for entry in "${clips[@]}"; do
+    name=${entry%%|*}
+    flags=${entry#*|}
+    if [[ ${#only[@]} -gt 0 && ! " ${only[*]} " =~ " $name " ]]; then continue; fi
+    dst="$out/$name.mkv"
+    if [[ -f $dst && $force = 0 ]]; then echo "skip $name (exists, --force to redo)"; continue; fi
+    echo "render $name ($size, ${seconds}s @ ${fps}fps)"
+    # shellcheck disable=SC2086
+    "$root/target/release/mandelbrot" --headless --antialias $flags \
+        --width "$w" --height "$h" --fps "$fps" --duration "$seconds" --export-path - |
+        ffmpeg -hide_banner -loglevel error -y \
+            -f rawvideo -pix_fmt rgba -s "$size" -framerate "$fps" -i - \
+            -vf "scale=out_color_matrix=bt709:out_range=tv:flags=accurate_rnd+full_chroma_int+bitexact,format=yuv420p10le" \
+            -c:v ffv1 -level 3 -slices 16 -g 1 \
+            -colorspace bt709 -color_primaries bt709 -color_trc bt709 -color_range tv \
+            "$dst.tmp.mkv"
+    mv "$dst.tmp.mkv" "$dst"
+done

tools/encode/sweep.sh

@@ -0,0 +1,87 @@
+#!/usr/bin/env bash
+# Encode every test clip with every config, then score each encode.
+#
+#   tools/encode/sweep.sh [--clips a,b] [--keep] [--tag NAME] CONFIG_FILE...
+#
+# A config line is `name | ffmpeg output args` (blank lines and # comments are
+# skipped). The args go between `-i clip.mkv` and the output file, e.g.
+#   x265-crf18 | -c:v libx265 -preset medium -crf 18 -x265-params aq-mode=3
+# Each row of results/<tag>.tsv has encode fps, bitrate, VMAF 4K (mean, 1st
+# percentile, min), VMAF-NEG mean, CAMBI banding (mean, max) and PSNR-Y.
+set -euo pipefail
+
+here=$(cd "$(dirname "$0")" && pwd)
+clipdir="$here/clips"
+model=/usr/share/model
+export SVT_LOG=1  # errors only
+clips=""
+keep=0
+tag=$(date +%Y%m%d-%H%M%S)
+configs=()
+
+while [[ $# -gt 0 ]]; do
+    case $1 in
+        --clips) clips=$2; shift 2 ;;
+        --keep) keep=1; shift ;;
+        --tag) tag=$2; shift 2 ;;
+        -h|--help) sed -n '2,11p' "$0"; exit 0 ;;
+        *) configs+=("$1"); shift ;;
+    esac
+done
+[[ ${#configs[@]} -gt 0 ]] || { echo "usage: $0 [--clips a,b] [--keep] [--tag NAME] CONFIG_FILE..." >&2; exit 1; }
+
+if [[ -z $clips ]]; then
+    clips=$(cd "$clipdir" && ls ./*.mkv | sed 's|^\./||; s|\.mkv$||' | paste -sd,)
+fi
+[[ -n $clips ]] || { echo "no clips in $clipdir: run make_clips.sh first" >&2; exit 1; }
+
+mkdir -p "$here/results" "$here/work"
+tsv="$here/results/$tag.tsv"
+[[ -f $tsv ]] || printf 'clip\tconfig\tfps\tmbps\tvmaf\tvmaf_p1\tvmaf_min\tvmaf_neg\tcambi\tcambi_max\tpsnr_y\n' > "$tsv"
+
+IFS=, read -ra clip_list <<< "$clips"
+for cfg in "${configs[@]}"; do
+    while IFS= read -r line || [[ -n $line ]]; do
+        [[ $line =~ ^[[:space:]]*(#|$) ]] && continue
+        name=$(sed 's/[[:space:]]*|.*//' <<< "$line")
+        args=$(sed 's/^[^|]*|[[:space:]]*//' <<< "$line")
+        for clip in "${clip_list[@]}"; do
+            ref="$clipdir/$clip.mkv"
+            enc="$here/work/$clip--$name.mp4"
+            log="$here/work/$clip--$name.json"
+            frames=$(ffprobe -v error -count_packets -select_streams v:0 \
+                -show_entries stream=nb_read_packets -of csv=p=0 "$ref")
+            printf '%-10s %-40s ' "$clip" "$name"
+
+            t0=$(date +%s.%N)
+            # shellcheck disable=SC2086
+            ffmpeg -hide_banner -loglevel error -y -i "$ref" $args -an "$enc" < /dev/null
+            t1=$(date +%s.%N)
+
+            # 4K model for both VMAF variants; CAMBI flags banding, which VMAF
+            # barely sees and which is the main risk on smooth fractal gradients.
+            ffmpeg -hide_banner -loglevel error -i "$enc" -i "$ref" -lavfi \
+                "[0:v]setpts=PTS-STARTPTS[d];[1:v]setpts=PTS-STARTPTS[r];[d][r]libvmaf=log_fmt=json:log_path=$log:n_threads=$(nproc):n_subsample=2:model='path=$model/vmaf_4k_v0.6.1.json\\:name=vmaf|path=$model/vmaf_4k_v0.6.1neg.json\\:name=neg':feature='name=cambi|name=psnr'" \
+                -f null - < /dev/null
+
+            row=$(python3 - "$log" "$enc" "$frames" "$t0" "$t1" <<'PY'
+import json, os, sys
+log, enc, frames, t0, t1 = sys.argv[1], sys.argv[2], int(sys.argv[3]), float(sys.argv[4]), float(sys.argv[5])
+fr = json.load(open(log))["frames"]
+col = lambda k: sorted(f["metrics"][k] for f in fr)
+v = col("vmaf")
+p1 = v[max(0, int(0.01 * len(v)) - 1)] if len(v) >= 100 else v[0]
+mean = lambda xs: sum(xs) / len(xs)
+cambi = col("cambi")
+fps = frames / (t1 - t0)
+mbps = os.path.getsize(enc) * 8 / (frames / 60) / 1e6
+print(f"{fps:.2f}\t{mbps:.1f}\t{mean(v):.2f}\t{p1:.2f}\t{v[0]:.2f}\t{mean(col('neg')):.2f}\t{mean(cambi):.2f}\t{cambi[-1]:.2f}\t{mean(col('psnr_y')):.2f}")
+PY
+)
+            printf '%s\t%s\t%s\n' "$clip" "$name" "$row" >> "$tsv"
+            awk -F'\t' '{printf "%6s fps %7s Mb/s  vmaf %s p1 %s min %s neg %s  cambi %s/%s  psnr %s\n",$1,$2,$3,$4,$5,$6,$7,$8,$9}' <<< "$row"
+            [[ $keep = 1 ]] || rm -f "$enc"
+        done
+    done < "$cfg"
+done
+echo "results: $tsv"