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 dashu-float), 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

cargo run --release          # native, run (release matters: fractal math is hot)
cargo test                   # reference-orbit math, share-link round-trip, WGSL validation
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)

Web build (WebGPU):

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
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, --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. 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. 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_jobs are snapshotted up front and RefJob::computed 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/view.rs — ViewState; center is arbitrary-precision FBig (Big type alias). 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 + FBig) 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 FBig 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 FBig 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).

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