feat: BLA iteration-skipping for deep-zoom Mandelbrot

CLAUDE.md

@@ -1,139 +0,0 @@
-# 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. The `f32` GPU tier reaches roughly 10³⁰×. 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 --test shader_valid   # just the WGSL parse/validate tests (naga, no GPU needed)
-cargo clippy
-cargo fmt                    # rustfmt.toml just pins edition = "2024"
-```
-
-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
-python3 -m http.server -d dist 8080
-```
-
-Native CLI flags (`src/cli.rs`, applied in `FractalApp::apply_cli`): `--kind`,
-`--power`, `--julia re,im`, `--share <fragment>`,
-`--view re,im,half_height[,iterations]`, `--de`, `--buddhabrot`,
-`--buddha-palette`, `--export` (+ `--export-path out.png`). `--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) — implies `--export`'s
-save behavior without needing a GPU-backed window/event loop. Not yet
-supported with `--buddhabrot`. Run `mandelbrot --help` for the full list.
-
-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), pixel scale stays `f64` (still in-range at 10³⁰×). Precision
-  (bits) scales with zoom depth (`precision_for`).
-- `src/fractal/reference.rs` — `FractalKind` enum (Mandelbrot, Burning Ship,
-  Tricorn, Multibrot, Celtic, Perpendicular, Buffalo, Phoenix, Lambda) and
-  `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.
-- `src/shaders/mandelbrot.wgsl` — the perturbation fragment shader.
-  `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 here must match the matching
-  `FractalKind` variant's discriminant exactly.
-- `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), 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 "morph c/p/λ" and auto-zoom animations),
-  `default_view_for` (per-kind starting view). `KINDS`, `JULIA_PRESETS`, and
-  `SET_PRESETS` are sized as `[T; FractalKind::<last variant> as usize + 1]` —
-  adding a new `FractalKind` means bumping all three (and adding an empty
-  `&[]` slot to the two preset arrays if the kind has none).
-- `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: `reference.rs` (enum variant + CPU iteration formula, and a
-test comparing against a naive `f64` iteration), `mandelbrot.wgsl` (matching
-`KIND_*` const + `advance_delta`/`fprime` arms), `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`), `share.rs` (encode/decode string tag), `app.rs` (`KINDS` label,
-`JULIA_PRESETS`/`SET_PRESETS` slot, `default_view_for` entry, 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). 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

@@ -8,16 +8,14 @@ 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"] }
 egui = "0.36.2"
+futures-channel = { version = "0.3.34", default-features = false, features = ["alloc", "std"] }
 log = "0.4.34"
 png = "0.18.1"
 
 [target.'cfg(not(target_arch = "wasm32"))'.dependencies]
 env_logger = "0.11.11"
-clap = { version = "4.5.51", features = ["derive"] }
-pollster = "1.0.1"
 
 [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"
@@ -28,8 +26,6 @@ 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,
 # egui) so the explorer is actually interactive during development.

build-web.sh

@@ -20,7 +20,6 @@ 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/cli.rs

@@ -1,98 +0,0 @@
-// 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>,
-
-    /// Exponent for the Multibrot kind (z -> z^power + c), clamped to [2, 8].
-    #[arg(long)]
-    pub power: Option<u32>,
-
-    /// Start in Julia mode with this seed constant.
-    #[arg(long, value_name = "RE,IM")]
-    pub julia: 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>,
-
-    /// Enable distance-estimation shading.
-    #[arg(long)]
-    pub de: bool,
-
-    /// Switch to the Buddhabrot renderer.
-    #[arg(long)]
-    pub buddhabrot: bool,
-
-    /// Buddhabrot tonemap palette index.
-    #[arg(long, value_name = "INDEX")]
-    pub buddha_palette: Option<u32>,
-
-    /// Render a PNG export on startup.
-    #[arg(long)]
-    pub export: bool,
-
-    /// Output path for --export/--headless (default: fractal-<timestamp>.png).
-    #[arg(long, value_name = "PATH")]
-    pub export_path: Option<String>,
-
-    /// 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. 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,
-}
-
-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,
-        }
-    }
-}

src/fractal/buddhabrot.rs

@@ -1,379 +0,0 @@
-//! 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 eframe::egui_wgpu::{self, 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,
-    pub _pad: [u32; 3],
-}
-
-/// 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,
-    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,
-            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 {
-    compute_pipeline: 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 = device.create_shader_module(wgpu::ShaderModuleDescriptor {
-            label: Some("buddhabrot"),
-            source: wgpu::ShaderSource::Wgsl(include_str!("../shaders/buddhabrot.wgsl").into()),
-        });
-
-        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 compute_pipeline = device.create_compute_pipeline(&wgpu::ComputePipelineDescriptor {
-            label: Some("buddhabrot compute pipeline"),
-            layout: Some(&compute_pipeline_layout),
-            module: &shader,
-            entry_point: Some("cs_main"),
-            compilation_options: Default::default(),
-            cache: None,
-        });
-
-        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 {
-            compute_pipeline,
-            compute_bind_group_layout,
-            tonemap_pipeline,
-            tonemap_bind_group_layout,
-            uniform_buffer,
-            histogram: None,
-            last_content: None,
-            total_samples: 0.0,
-            seed: 0,
-        }
-    }
-
-    /// 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],
-}
-
-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 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(&renderer.compute_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/mod.rs

@@ -1,16 +1,13 @@
 //! GPU fractal rendering: wgpu pipeline, uniforms, reference orbit, and the
 //! egui paint callback.
 
-pub mod buddhabrot;
 pub mod reference;
 pub mod renderer;
 pub mod share;
 
-pub use buddhabrot::{BuddhabrotCallback, BuddhabrotRenderer, BuddhabrotUniforms};
-pub use reference::{FractalKind, compute_reference, compute_set_reference};
-#[cfg(target_arch = "wasm32")]
-pub use renderer::encode_png_with_progress;
-#[cfg(not(target_arch = "wasm32"))]
-pub use renderer::export_to_png_blocking;
-pub use renderer::{ExportRender, FractalCallback, FractalRenderer, MAX_REF_POINTS, Uniforms};
+pub use reference::{Bla, FractalKind, build_bla_table, compute_reference, compute_set_reference};
+pub use renderer::{
+    ExportRender, FractalCallback, FractalRenderer, MAX_REF_POINTS, Uniforms,
+    encode_png_with_progress,
+};
 pub use share::ShareState;

src/fractal/reference.rs

@@ -10,31 +10,32 @@
 //! * Mandelbrot-set: `z0 = 0`, `c = view center` (the c-plane point per pixel).
 //! * Julia-set:      `z0 = view center`, `c = fractal constant` (fixed per view).
 
-use crate::view::{Big, big_from_f64};
+use crate::view::Big;
 
 /// 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,
+    Mandelbrot,
     /// `z -> (|Re z| + i|Im z|)^2 + c`.
-    BurningShip = 1,
+    BurningShip,
     /// `z -> conj(z)^2 + c` (the Mandelbar).
-    Tricorn = 2,
+    Tricorn,
     /// `z -> z^power + c` (power >= 2).
-    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)` (logistic map).
-    Lambda = 8,
+    Multibrot,
+}
+
+impl FractalKind {
+    /// Integer id matching the shader's `KIND_*` constants.
+    pub fn shader_id(self) -> u32 {
+        match self {
+            FractalKind::Mandelbrot => 0,
+            FractalKind::BurningShip => 1,
+            FractalKind::Tricorn => 2,
+            FractalKind::Multibrot => 3,
+        }
+    }
 }
 
 /// Reference orbit escapes once |Z|^2 exceeds this. Kept larger than the pixel
@@ -45,7 +46,6 @@ const REFERENCE_ESCAPE_SQ: f64 = 1.0e10;
 /// Compute the reference orbit `Z_0..Z_{len-1}` where `Z_0 = z0` and
 /// `Z_{n+1} = f(Z_n, c)` for the given `kind` (and `power`, for Multibrot), up
 /// to `max_iter` steps at `precision` bits. Each entry is `[re, im]` in f32.
-#[allow(clippy::too_many_arguments)]
 pub fn compute_reference(
     z0_re: &Big,
     z0_im: &Big,
@@ -55,23 +55,12 @@ pub fn compute_reference(
     precision: usize,
     kind: FractalKind,
     power: u32,
-    phoenix_p: (f64, f64),
-    lambda_l: (f64, f64),
 ) -> Vec<[f32; 2]> {
     let cr = c_re.clone().with_precision(precision).value();
     let ci = c_im.clone().with_precision(precision).value();
 
     let mut zr = z0_re.clone().with_precision(precision).value();
     let mut zi = z0_im.clone().with_precision(precision).value();
-    // Previous iterate, for the Phoenix two-term recurrence (Y_{-1} = 0).
-    let mut zr_prev = big_zero(precision);
-    let mut zi_prev = big_zero(precision);
-    // Phoenix distortion constant `p` (a small fixed complex number).
-    let pr = big_from_f64(phoenix_p.0, precision);
-    let pi = big_from_f64(phoenix_p.1, precision);
-    // Lambda distortion constant `l` (a small fixed complex number).
-    let lr = big_from_f64(lambda_l.0, precision);
-    let li = big_from_f64(lambda_l.1, precision);
 
     let mut points: Vec<[f32; 2]> = Vec::with_capacity(max_iter as usize + 1);
 
@@ -108,45 +97,8 @@ pub fn compute_reference(
                 let (pr, pi) = complex_pow(&zr, &zi, power.max(2), precision);
                 (pr + &cr, pi + &ci)
             }
-            FractalKind::Celtic => {
-                // |Re(z^2)| + i·Im(z^2): abs the real output of the square.
-                let re = big_abs(&zr.sqr() - &zi.sqr()) + &cr;
-                let im = ((&zr * &zi) << 1) + &ci;
-                (re, im)
-            }
-            FractalKind::Perpendicular => {
-                // (x^2 - y^2) - 2·x·|y| i: abs the imaginary input.
-                let re = &zr.sqr() - &zi.sqr() + &cr;
-                let im = &ci - ((&zr * &big_abs(zi.clone())) << 1);
-                (re, im)
-            }
-            FractalKind::Buffalo => {
-                // |Re(z^2)| - |Im(z^2)| i: abs both outputs.
-                let re = big_abs(&zr.sqr() - &zi.sqr()) + &cr;
-                let im = &ci - big_abs((&zr * &zi) << 1);
-                (re, im)
-            }
-            FractalKind::Phoenix => {
-                // z^2 + c + p·z_{n-1}.
-                let re2 = &zr.sqr() - &zi.sqr();
-                let im2 = (&zr * &zi) << 1;
-                let pzr = &pr * &zr_prev - &pi * &zi_prev;
-                let pzi = &pr * &zi_prev + &pi * &zr_prev;
-                (re2 + &cr + pzr, im2 + &ci + pzi)
-            }
-            FractalKind::Lambda => {
-                // λ·z(1 - z): logistic map.
-                let re2 = 1 - &zr;
-                let im2 = -&zi;
-                let lzr = &lr * &zr - &li * &zi;
-                let lzi = &lr * &zi + &li * &zr;
-                (&lzr * &re2 - &lzi * &im2, re2 * lzi + lzr * im2)
-            }
         };
 
-        // Shift the previous iterate (only the Phoenix arm reads it).
-        zr_prev = zr;
-        zi_prev = zi;
         zr = new_zr.with_precision(precision).value();
         zi = new_zi.with_precision(precision).value();
     }
@@ -180,7 +132,6 @@ fn complex_pow(zr: &Big, zi: &Big, power: u32, precision: usize) -> (Big, Big) {
 
 /// Convenience: parameter-plane ("Mandelbrot-set") reference (`z0 = 0`,
 /// `c = center`) for any `kind`.
-#[allow(clippy::too_many_arguments)]
 pub fn compute_set_reference(
     center_re: &Big,
     center_im: &Big,
@@ -188,15 +139,157 @@ pub fn compute_set_reference(
     precision: usize,
     kind: FractalKind,
     power: u32,
-    phoenix_p: (f64, f64),
-    lambda_l: (f64, f64),
 ) -> Vec<[f32; 2]> {
     let zero = big_zero(precision);
     compute_reference(
-        &zero, &zero, center_re, center_im, max_iter, precision, kind, power, phoenix_p, lambda_l,
+        &zero, &zero, center_re, center_im, max_iter, precision, kind, power,
     )
 }
 
+// ---------------------------------------------------------------------------
+// Bivariate Linear Approximation (BLA)
+//
+// Deep in a zoom the per-pixel delta stays far smaller than the reference, so
+// the nonlinear `e^2` term of the perturbation step is negligible and the step
+// is effectively linear: `e -> A e + B dc`. BLA precomputes, for runs of
+// iterations, the composed linear coefficients `(A, B)` plus a validity radius
+// `r` (the largest `|e|` for which dropping `e^2` stays within tolerance). A
+// pixel can then skip a whole run in one multiply whenever `|e| < r`.
+//
+// Runs are merged pairwise into a binary tree of levels: level `k` holds BLAs of
+// length `2^k` starting at multiples of `2^k`. The GPU walks levels high→low to
+// take the longest valid skip at the current index. Both sides recompute the
+// per-level counts from `ref_len` (count[0] = ref_len-1, count[k] = count[k-1]/2)
+// so no offset table needs to travel to the GPU — only this flat array does.
+//
+// Only the holomorphic square map (Mandelbrot/Julia, `A = 2 Z`, `B = 1`) is
+// supported; other kinds fall back to per-iteration stepping on the GPU.
+// ---------------------------------------------------------------------------
+
+/// One merged linear step: `e_{n+l} = A e_n + B dc`, valid while `|e_n| < r`.
+/// Laid out to match the WGSL `Bla` struct (two `vec2<f32>`, then `f32`, `u32`;
+/// 24-byte std430 stride).
+#[repr(C)]
+#[derive(Clone, Copy, bytemuck::Pod, bytemuck::Zeroable)]
+pub struct Bla {
+    pub a: [f32; 2],
+    pub b: [f32; 2],
+    pub r: f32,
+    pub l: u32,
+}
+
+/// Relative budget for the dropped nonlinear term, chosen near the f32 orbit
+/// storage noise floor so BLA adds no visible error over plain perturbation.
+const BLA_EPS: f64 = 1.0e-6;
+
+/// f64 working form of a BLA (merges accumulate in f64, stored as f32).
+#[derive(Clone, Copy)]
+struct BlaF {
+    ar: f64,
+    ai: f64,
+    br: f64,
+    bi: f64,
+    r: f64,
+    l: u32,
+}
+
+impl BlaF {
+    fn to_bla(self) -> Bla {
+        Bla {
+            a: [self.ar as f32, self.ai as f32],
+            b: [self.br as f32, self.bi as f32],
+            r: self.r as f32,
+            l: self.l,
+        }
+    }
+}
+
+/// Merge two consecutive BLAs (`x` then `y`) into one covering both runs.
+fn merge_bla(x: BlaF, y: BlaF, dc_max: f64) -> BlaF {
+    // A = Ay Ax ; B = Ay Bx + By  (complex).
+    let ar = y.ar * x.ar - y.ai * x.ai;
+    let ai = y.ar * x.ai + y.ai * x.ar;
+    let br = y.ar * x.br - y.ai * x.bi + y.br;
+    let bi = y.ar * x.bi + y.ai * x.br + y.bi;
+    // Valid if |e| < rx (so x holds) and |Ax e + Bx dc| < ry (so y holds):
+    //   |e| < (ry - |Bx| dc_max) / |Ax|.
+    let ax_mag = (x.ar * x.ar + x.ai * x.ai).sqrt();
+    let bx_mag = (x.br * x.br + x.bi * x.bi).sqrt();
+    let r_y = if ax_mag > 0.0 {
+        ((y.r - bx_mag * dc_max) / ax_mag).max(0.0)
+    } else {
+        x.r
+    };
+    BlaF {
+        ar,
+        ai,
+        br,
+        bi,
+        r: x.r.min(r_y),
+        l: x.l + y.l,
+    }
+}
+
+/// Build the BLA table for a square-map reference orbit. `dc_max` is an upper
+/// bound on any pixel's `|dc|` in the current view (used to size merge radii).
+/// Returns a flat array with levels concatenated (level 0 first). Empty if the
+/// orbit is too short to skip.
+pub fn build_bla_table(points: &[[f32; 2]], dc_max: f64) -> Vec<Bla> {
+    let m = points.len();
+    if m < 2 {
+        return Vec::new();
+    }
+
+    // Level 0: one single step from each index i (uses Z_i). A = 2 Z, B = 1.
+    // Dropping e^2 is within tolerance while |e| < BLA_EPS |Z| (since the kept
+    // linear term is |2 Z e|).
+    let mut level0: Vec<BlaF> = Vec::with_capacity(m - 1);
+    for z in &points[..m - 1] {
+        let (zr, zi) = (z[0] as f64, z[1] as f64);
+        let zmag = (zr * zr + zi * zi).sqrt();
+        level0.push(BlaF {
+            ar: 2.0 * zr,
+            ai: 2.0 * zi,
+            br: 1.0,
+            bi: 0.0,
+            r: BLA_EPS * zmag,
+            l: 1,
+        });
+    }
+
+    let mut levels: Vec<Vec<BlaF>> = vec![level0];
+    while levels.last().unwrap().len() >= 2 {
+        let prev = levels.last().unwrap();
+        let mut next = Vec::with_capacity(prev.len() / 2);
+        let mut i = 0;
+        while i + 1 < prev.len() {
+            next.push(merge_bla(prev[i], prev[i + 1], dc_max));
+            i += 2;
+        }
+        levels.push(next);
+    }
+
+    let mut flat = Vec::with_capacity(levels.iter().map(|l| l.len()).sum());
+    for level in &levels {
+        flat.extend(level.iter().map(|b| b.to_bla()));
+    }
+    flat
+}
+
+/// Start offset of BLA level `lv` within the flat table, computed from the orbit
+/// length exactly as the shader does (`count[0] = ref_len-1`, halving each
+/// level). Kept here so the traversal test mirrors the GPU indexing.
+#[cfg(test)]
+fn bla_level_start(ref_len: usize, lv: u32) -> (usize, usize) {
+    let mut start = 0usize;
+    let mut count = ref_len - 1;
+    for _ in 0..lv {
+        start += count;
+        count /= 2;
+    }
+    (start, count)
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -207,16 +300,7 @@ mod tests {
     fn reference_matches_naive_f64() {
         let cr = Big::try_from(-0.75_f64).unwrap();
         let ci = Big::try_from(0.1_f64).unwrap();
-        let points = compute_set_reference(
-            &cr,
-            &ci,
-            60,
-            200,
-            FractalKind::Mandelbrot,
-            2,
-            (0.0, 0.0),
-            (0.0, 0.0),
-        );
+        let points = compute_set_reference(&cr, &ci, 60, 200, FractalKind::Mandelbrot, 2);
 
         // Independent naive f64 orbit.
         let (c_re, c_im) = (-0.75_f64, 0.1_f64);
@@ -226,14 +310,8 @@ mod tests {
             // significant figures.
             let tol_re = 1e-4 * (1.0 + zr.abs());
             let tol_im = 1e-4 * (1.0 + zi.abs());
-            assert!(
-                (point[0] as f64 - zr).abs() < tol_re,
-                "re mismatch: {point:?} vs {zr}"
-            );
-            assert!(
-                (point[1] as f64 - zi).abs() < tol_im,
-                "im mismatch: {point:?} vs {zi}"
-            );
+            assert!((point[0] as f64 - zr).abs() < tol_re, "re mismatch: {point:?} vs {zr}");
+            assert!((point[1] as f64 - zi).abs() < tol_im, "im mismatch: {point:?} vs {zi}");
             let nzr = zr * zr - zi * zi + c_re;
             let nzi = 2.0 * zr * zi + c_im;
             zr = nzr;
@@ -246,16 +324,7 @@ mod tests {
     fn interior_orbit_runs_full_length() {
         let cr = Big::try_from(-0.2_f64).unwrap();
         let ci = Big::try_from(0.0_f64).unwrap();
-        let points = compute_set_reference(
-            &cr,
-            &ci,
-            500,
-            120,
-            FractalKind::Mandelbrot,
-            2,
-            (0.0, 0.0),
-            (0.0, 0.0),
-        );
+        let points = compute_set_reference(&cr, &ci, 500, 120, FractalKind::Mandelbrot, 2);
         assert_eq!(points.len(), 501, "interior orbit should not escape");
     }
 
@@ -264,16 +333,7 @@ mod tests {
     fn burning_ship_reference_matches_naive_f64() {
         let cr = Big::try_from(-1.75_f64).unwrap();
         let ci = Big::try_from(-0.03_f64).unwrap();
-        let points = compute_set_reference(
-            &cr,
-            &ci,
-            60,
-            200,
-            FractalKind::BurningShip,
-            2,
-            (0.0, 0.0),
-            (0.0, 0.0),
-        );
+        let points = compute_set_reference(&cr, &ci, 60, 200, FractalKind::BurningShip, 2);
 
         let (c_re, c_im) = (-1.75_f64, -0.03_f64);
         let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -293,16 +353,7 @@ mod tests {
     fn multibrot3_reference_matches_naive_f64() {
         let cr = Big::try_from(0.3_f64).unwrap();
         let ci = Big::try_from(0.2_f64).unwrap();
-        let points = compute_set_reference(
-            &cr,
-            &ci,
-            60,
-            200,
-            FractalKind::Multibrot,
-            3,
-            (0.0, 0.0),
-            (0.0, 0.0),
-        );
+        let points = compute_set_reference(&cr, &ci, 60, 200, FractalKind::Multibrot, 3);
 
         let (c_re, c_im) = (0.3_f64, 0.2_f64);
         let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -335,8 +386,6 @@ mod tests {
             200,
             FractalKind::Mandelbrot,
             2,
-            (0.0, 0.0),
-            (0.0, 0.0),
         );
 
         let (mut zr, mut zi) = (0.15_f64, -0.1_f64);
@@ -352,121 +401,125 @@ mod tests {
         }
     }
 
-    /// Celtic reference matches a naive f64 iteration: real = |x^2 - y^2| + cr.
+    /// Step-by-step perturbation (drops nothing): `e_{n+1} = 2 Z_n e_n + e_n^2 + dc`,
+    /// using the stored f32 orbit as `Z_n`. Returns `e` after `target_n` steps.
+    fn advance_naive(points: &[[f32; 2]], dc: (f64, f64), target_n: usize) -> (f64, f64) {
+        let (mut er, mut ei) = (0.0f64, 0.0f64);
+        for z in &points[..target_n] {
+            let (zr, zi) = (z[0] as f64, z[1] as f64);
+            let tr = 2.0 * (zr * er - zi * ei);
+            let ti = 2.0 * (zr * ei + zi * er);
+            let sr = er * er - ei * ei;
+            let si = 2.0 * er * ei;
+            er = tr + sr + dc.0;
+            ei = ti + si + dc.1;
+        }
+        (er, ei)
+    }
+
+    /// Advance `e` to exactly `target_n` steps using the BLA table — the same
+    /// walk the shader performs (longest valid skip first, else a full step),
+    /// but never skipping past `target_n`. Returns `(e, took_a_multi_step_skip)`.
+    fn advance_bla(
+        points: &[[f32; 2]],
+        table: &[Bla],
+        dc: (f64, f64),
+        target_n: usize,
+    ) -> ((f64, f64), bool) {
+        let ref_len = points.len();
+        let (mut er, mut ei) = (0.0f64, 0.0f64);
+        let mut n = 0usize;
+        let mut skipped = false;
+
+        while n < target_n {
+            let emag2 = er * er + ei * ei;
+            let mut applied = false;
+
+            // Highest level worth trying is bounded by how far we may advance.
+            let span = target_n - n;
+            let max_lv = (usize::BITS - 1 - span.leading_zeros()) as i64; // floor(log2(span))
+            let mut lv = max_lv;
+            while lv >= 0 {
+                let lvu = lv as u32;
+                let step = 1usize << lvu;
+                if n % step == 0 && n + step <= target_n {
+                    let (start, count) = bla_level_start(ref_len, lvu);
+                    let idx = n >> lvu;
+                    if idx < count {
+                        let b = table[start + idx];
+                        let r = b.r as f64;
+                        if emag2 < r * r {
+                            let (ar, ai) = (b.a[0] as f64, b.a[1] as f64);
+                            let (br, bi) = (b.b[0] as f64, b.b[1] as f64);
+                            let ner = ar * er - ai * ei + br * dc.0 - bi * dc.1;
+                            let nei = ar * ei + ai * er + br * dc.1 + bi * dc.0;
+                            er = ner;
+                            ei = nei;
+                            n += step;
+                            skipped |= step > 1;
+                            applied = true;
+                            break;
+                        }
+                    }
+                }
+                lv -= 1;
+            }
+
+            if !applied {
+                let (zr, zi) = (points[n][0] as f64, points[n][1] as f64);
+                let tr = 2.0 * (zr * er - zi * ei);
+                let ti = 2.0 * (zr * ei + zi * er);
+                let sr = er * er - ei * ei;
+                let si = 2.0 * er * ei;
+                er = tr + sr + dc.0;
+                ei = ti + si + dc.1;
+                n += 1;
+            }
+        }
+        ((er, ei), skipped)
+    }
+
+    /// The BLA walk must reproduce step-by-step perturbation at deep zoom (where
+    /// the delta is tiny and skips actually fire).
     #[test]
-    fn celtic_reference_matches_naive_f64() {
-        let cr = Big::try_from(-0.6_f64).unwrap();
-        let ci = Big::try_from(0.4_f64).unwrap();
-        let points = compute_set_reference(
-            &cr,
-            &ci,
-            60,
-            200,
-            FractalKind::Celtic,
-            2,
-            (0.0, 0.0),
-            (0.0, 0.0),
-        );
-
-        let (c_re, c_im) = (-0.6_f64, 0.4_f64);
-        let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
-        for point in &points {
-            let tol = 1e-4 * (1.0 + zr.abs().max(zi.abs()));
-            assert!((point[0] as f64 - zr).abs() < tol, "re: {point:?} vs {zr}");
-            assert!((point[1] as f64 - zi).abs() < tol, "im: {point:?} vs {zi}");
-            let nzr = (zr * zr - zi * zi).abs() + c_re;
-            let nzi = 2.0 * zr * zi + c_im;
-            zr = nzr;
-            zi = nzi;
-        }
-    }
-
-    /// Perpendicular reference matches a naive f64 iteration:
-    /// real = x^2 - y^2 + cr, imag = -2·x·|y| + ci.
-    #[test]
-    fn perpendicular_reference_matches_naive_f64() {
-        let cr = Big::try_from(-0.7_f64).unwrap();
-        let ci = Big::try_from(-0.2_f64).unwrap();
-        let points = compute_set_reference(
-            &cr,
-            &ci,
-            60,
-            200,
-            FractalKind::Perpendicular,
-            2,
-            (0.0, 0.0),
-            (0.0, 0.0),
-        );
-
-        let (c_re, c_im) = (-0.7_f64, -0.2_f64);
-        let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
-        for point in &points {
-            let tol = 1e-4 * (1.0 + zr.abs().max(zi.abs()));
-            assert!((point[0] as f64 - zr).abs() < tol, "re: {point:?} vs {zr}");
-            assert!((point[1] as f64 - zi).abs() < tol, "im: {point:?} vs {zi}");
-            let nzr = zr * zr - zi * zi + c_re;
-            let nzi = -2.0 * zr * zi.abs() + c_im;
-            zr = nzr;
-            zi = nzi;
-        }
-    }
-
-    /// Buffalo reference matches a naive f64 iteration:
-    /// real = |x^2 - y^2| + cr, imag = -|2·x·y| + ci.
-    #[test]
-    fn buffalo_reference_matches_naive_f64() {
-        let cr = Big::try_from(-1.2_f64).unwrap();
-        let ci = Big::try_from(-0.35_f64).unwrap();
-        let points = compute_set_reference(
-            &cr,
-            &ci,
-            60,
-            200,
-            FractalKind::Buffalo,
-            2,
-            (0.0, 0.0),
-            (0.0, 0.0),
-        );
-
-        let (c_re, c_im) = (-1.2_f64, -0.35_f64);
-        let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
-        for point in &points {
-            let tol = 1e-4 * (1.0 + zr.abs().max(zi.abs()));
-            assert!((point[0] as f64 - zr).abs() < tol, "re: {point:?} vs {zr}");
-            assert!((point[1] as f64 - zi).abs() < tol, "im: {point:?} vs {zi}");
-            let nzr = (zr * zr - zi * zi).abs() + c_re;
-            let nzi = -(2.0 * zr * zi).abs() + c_im;
-            zr = nzr;
-            zi = nzi;
-        }
-    }
-
-    /// Phoenix reference matches a naive f64 two-term iteration
-    /// `z_{n+1} = z_n^2 + c + p·z_{n-1}` (z_0 = 0, z_{-1} = 0).
-    #[test]
-    fn phoenix_reference_matches_naive_f64() {
-        let cr = Big::try_from(0.5667_f64).unwrap();
+    fn bla_matches_step_by_step() {
+        // An interior center (never escapes), so `e` stays bounded and we can
+        // iterate the full orbit; zoomed so |dc| ~ 1e-9 (deep enough for big
+        // skips). Correctness of the walk is independent of which orbit we pick.
+        let cr = Big::try_from(-0.5_f64).unwrap();
         let ci = Big::try_from(0.0_f64).unwrap();
-        let p = (-0.5_f64, 0.0_f64);
-        let points =
-            compute_set_reference(&cr, &ci, 60, 200, FractalKind::Phoenix, 2, p, (0.0, 0.0));
+        let points = compute_set_reference(&cr, &ci, 800, 160, FractalKind::Mandelbrot, 2);
+        assert!(points.len() > 64, "need a long orbit to exercise BLA levels");
 
-        let (c_re, c_im) = (0.5667_f64, 0.0_f64);
-        let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
-        let (mut pr, mut pi) = (0.0_f64, 0.0_f64); // previous iterate
-        for point in &points {
-            let tol = 1e-4 * (1.0 + zr.abs().max(zi.abs()));
-            assert!((point[0] as f64 - zr).abs() < tol, "re: {point:?} vs {zr}");
-            assert!((point[1] as f64 - zi).abs() < tol, "im: {point:?} vs {zi}");
-            // p·z_{n-1} = (p.0 + i p.1)(pr + i pi).
-            let pzr = p.0 * pr - p.1 * pi;
-            let pzi = p.0 * pi + p.1 * pr;
-            let nzr = zr * zr - zi * zi + c_re + pzr;
-            let nzi = 2.0 * zr * zi + c_im + pzi;
-            pr = zr;
-            pi = zi;
-            zr = nzr;
-            zi = nzi;
+        let half_height = 1.0e-9_f64;
+        let aspect = 1.5_f64;
+        let dc_max = half_height * (1.0 + aspect * aspect).sqrt();
+        let table = build_bla_table(&points, dc_max);
+        assert!(!table.is_empty());
+
+        let target_n = points.len() - 1;
+        // A few pixel offsets across the view (all within dc_max).
+        let offsets = [
+            (0.0, 0.0),
+            (0.6e-9, -0.4e-9),
+            (-0.9e-9, 0.3e-9),
+            (0.2e-9, 0.8e-9),
+        ];
+        let mut any_skip = false;
+        for dc in offsets {
+            let naive = advance_naive(&points, dc, target_n);
+            let (bla, skipped) = advance_bla(&points, &table, dc, target_n);
+            any_skip |= skipped;
+
+            let ref_mag = (naive.0 * naive.0 + naive.1 * naive.1).sqrt();
+            let err = ((bla.0 - naive.0).powi(2) + (bla.1 - naive.1).powi(2)).sqrt();
+            // Only the dropped e^2 differs; must stay near the BLA_EPS budget.
+            let tol = 1e-4 * ref_mag + 1e-15;
+            assert!(
+                err <= tol,
+                "dc={dc:?}: BLA {bla:?} vs naive {naive:?} (err {err:e} > tol {tol:e})"
+            );
         }
+        assert!(any_skip, "BLA never took a multi-step skip — test is not exercising it");
     }
 }

src/fractal/renderer.rs

@@ -13,43 +13,79 @@ use std::sync::Arc;
 
 use eframe::egui_wgpu::{self, wgpu};
 
-use crate::lights::{Light, MAX_LIGHT_COUNT};
+use super::reference::Bla;
 
 /// Maximum reference-orbit length (points) the storage buffer can hold. Also
 /// bounds the iteration count. 128k points * 8 bytes = 1 MiB.
 pub const MAX_REF_POINTS: usize = 1 << 17;
 
-/// Format of the intermediate iteration-data texture holding, per pixel,
-/// `(ci, DE factor, interior fraction)`. 32-bit float keeps the smooth iteration
-/// count precise at deep zoom. Color-renderable and read with nearest sampling
-/// (iteration data must never be linearly filtered across escape boundaries), so
-/// no `float32-filterable` feature is needed.
-const DATA_FORMAT: wgpu::TextureFormat = wgpu::TextureFormat::Rgba32Float;
+/// Maximum BLA-table entries the storage buffer can hold. A full table has
+/// ~2× the orbit length (all levels summed); ~256k entries * 24 bytes = 6 MiB.
+pub const MAX_BLA_ENTRIES: usize = 2 * MAX_REF_POINTS;
 
-/// True when the two uniforms differ in any field the iteration pass depends on
-/// (i.e. anything except the palette / colour scale / offset).
-fn geom_differs(a: &Uniforms, b: &Uniforms) -> bool {
-    a.span != b.span
-        || a.max_iter != b.max_iter
-        || a.ref_len != b.ref_len
-        || a.bailout_sq != b.bailout_sq
-        || a.is_julia != b.is_julia
-        || a.aa_level != b.aa_level
-        || a.kind != b.kind
-        || a.power != b.power
-        || a.dc_offset != b.dc_offset
-        || a.phoenix_p != b.phoenix_p
-        || a.de_coloring != b.de_coloring
+/// The fractal pipeline's bind group layout: uniforms (0), reference orbit (1),
+/// BLA table (2). Shared by the live renderer and [`ExportRender`].
+fn fractal_bind_group_layout_desc<'a>() -> wgpu::BindGroupLayoutDescriptor<'a> {
+    const STORAGE: wgpu::BindingType = wgpu::BindingType::Buffer {
+        ty: wgpu::BufferBindingType::Storage { read_only: true },
+        has_dynamic_offset: false,
+        min_binding_size: None,
+    };
+    wgpu::BindGroupLayoutDescriptor {
+        label: Some("fractal 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: 1,
+                visibility: wgpu::ShaderStages::FRAGMENT,
+                ty: STORAGE,
+                count: None,
+            },
+            wgpu::BindGroupLayoutEntry {
+                binding: 2,
+                visibility: wgpu::ShaderStages::FRAGMENT,
+                ty: STORAGE,
+                count: None,
+            },
+        ],
+    }
 }
 
-/// True when the two uniforms differ in a colour-only field (remappable by the
-/// cheap colourise pass without re-iterating).
-fn color_differs(a: &Uniforms, b: &Uniforms) -> bool {
-    a.color_offset != b.color_offset
-        || a.color_scale != b.color_scale
-        || a.palette_id != b.palette_id
-        || a.shadow_palette_id != b.shadow_palette_id
-        || a.shadow != b.shadow
+/// Build the fractal bind group from its three buffers.
+fn fractal_bind_group(
+    device: &wgpu::Device,
+    layout: &wgpu::BindGroupLayout,
+    uniform_buffer: &wgpu::Buffer,
+    ref_buffer: &wgpu::Buffer,
+    bla_buffer: &wgpu::Buffer,
+) -> wgpu::BindGroup {
+    device.create_bind_group(&wgpu::BindGroupDescriptor {
+        label: Some("fractal bind group"),
+        layout,
+        entries: &[
+            wgpu::BindGroupEntry {
+                binding: 0,
+                resource: uniform_buffer.as_entire_binding(),
+            },
+            wgpu::BindGroupEntry {
+                binding: 1,
+                resource: ref_buffer.as_entire_binding(),
+            },
+            wgpu::BindGroupEntry {
+                binding: 2,
+                resource: bla_buffer.as_entire_binding(),
+            },
+        ],
+    })
 }
 
 /// GPU-side view + coloring parameters. Layout must match `Uniforms` in the
@@ -68,92 +104,60 @@ pub struct Uniforms {
     /// 0 = Mandelbrot, 1 = Julia.
     pub is_julia: u32,
     pub palette_id: u32,
-    pub shadow_palette_id: u32,
     /// Supersampling factor per axis: 1 = off, 2 = 2×2 (4 samples).
     pub aa_level: u32,
     /// Iteration formula (`FractalKind::shader_id`).
     pub kind: u32,
     /// Exponent for the Multibrot kind.
     pub power: u32,
-    pub _pad: [u32; 1],
     /// Complex offset of the view center from the reference center, so a stale
     /// or reused reference (computed at a slightly different center) still maps
     /// correctly. Added to every pixel's per-pixel offset.
     pub dc_offset: [f32; 2],
-    /// Distortion constant `p` for the Phoenix map (`z^2 + c + p·z_{n-1}`);
-    /// ignored by other kinds. Kept next to `dc_offset` so both `vec2`s land on
-    /// 8-byte boundaries, matching the shader's layout.
-    pub phoenix_p: [f32; 2],
-    /// Distortion constant `l` for the Lambda map (`l·z(1 - z)`);
-    /// ignored by other kinds.
-    pub lambda_l: [f32; 2],
     /// 0 = escape-time coloring, 1 = distance-estimation shading.
     pub de_coloring: u32,
-    // 0 = classic colors, 1 = shadows
-    pub shadow: u32,
+    /// 0 = per-iteration stepping, 1 = BLA iteration-skipping (square map only).
+    /// This also fills the struct out to a 16-byte multiple (uniform requirement).
+    pub use_bla: u32,
 }
 
-/// Offscreen textures for the two-pass render, recreated whenever the widget's
-/// pixel size changes:
-/// * `data_view` — the iteration pass's output (see [`DATA_FORMAT`]).
-/// * `color_view` — the colourise pass's output; the blit source.
-///   plus the bind groups that read them.
+/// Offscreen texture the fractal is rendered into, plus the bind group used to
+/// blit it. Recreated whenever the widget's pixel size changes.
 struct CacheTarget {
-    data_view: wgpu::TextureView,
-    color_view: wgpu::TextureView,
-    /// Colourise pass input: uniforms + the data texture.
-    colorize_bind_group: wgpu::BindGroup,
-    /// Blit pass input: the colour texture + sampler.
+    view: wgpu::TextureView,
     blit_bind_group: wgpu::BindGroup,
     width: u32,
     height: u32,
 }
 
-/// What the iteration-data texture was last computed with. If the next frame's
-/// geometry inputs match, iteration is skipped and only colour may be redone.
-struct IterState {
+/// State the cache texture was last rendered with. If the next frame's inputs
+/// match this, the cache is still valid and the fractal shader is skipped.
+struct RenderedState {
     uniforms: Uniforms,
     generation: u64,
     width: u32,
     height: u32,
 }
 
-/// What the colour texture was last computed with. If the next frame's colour
-/// inputs (and size) match and iteration did not re-run, colourise is skipped.
-struct ColorState {
-    uniforms: Uniforms,
-    width: u32,
-    height: u32,
-}
-
 pub struct FractalRenderer {
-    /// Iteration pass: perturbation iterate → data texture (`fs_data`).
-    iterate_pipeline: wgpu::RenderPipeline,
-    /// Combined iterate + colour in one pass (`fs_color`), used only by export.
-    export_pipeline: wgpu::RenderPipeline,
+    pipeline: wgpu::RenderPipeline,
     bind_group_layout: wgpu::BindGroupLayout,
     uniform_buffer: wgpu::Buffer,
     ref_buffer: wgpu::Buffer,
-    lights_buffer: wgpu::Buffer,
+    bla_buffer: wgpu::Buffer,
     bind_group: wgpu::BindGroup,
     target_format: wgpu::TextureFormat,
-    /// Generation of the reference orbit currently uploaded to `ref_buffer`.
+    /// Generation of the reference orbit + BLA table currently uploaded.
     uploaded_generation: u64,
 
-    /// Colourise pass: data texture → colour texture (palette mapping).
-    colorize_pipeline: wgpu::RenderPipeline,
-    colorize_bind_group_layout: wgpu::BindGroupLayout,
-
-    /// Blit pipeline + resources that copy the colour texture to egui's surface.
+    /// Blit pipeline + resources that copy the cache texture to egui's surface.
     blit_pipeline: wgpu::RenderPipeline,
     blit_bind_group_layout: wgpu::BindGroupLayout,
     blit_sampler: wgpu::Sampler,
-    /// The offscreen textures; `None` until the first frame sizes them.
+    /// The offscreen cache; `None` until the first frame sizes it.
     cache: Option<CacheTarget>,
-    /// What the data texture holds; `None` forces re-iteration.
-    iterated: Option<IterState>,
-    /// What the colour texture holds; `None` forces a recolour.
-    colored: Option<ColorState>,
+    /// What the cache currently holds; `None` forces a re-render.
+    rendered: Option<RenderedState>,
 }
 
 impl FractalRenderer {
@@ -177,53 +181,23 @@ impl FractalRenderer {
             mapped_at_creation: false,
         });
 
-        let lights_buffer = device.create_buffer(&wgpu::BufferDescriptor {
-            label: Some("lights parameters"),
-            size: (MAX_LIGHT_COUNT * std::mem::size_of::<Light>()) as u64,
-            usage: wgpu::BufferUsages::UNIFORM | wgpu::BufferUsages::COPY_DST,
+        let bla_buffer = device.create_buffer(&wgpu::BufferDescriptor {
+            label: Some("bla table"),
+            size: (MAX_BLA_ENTRIES * std::mem::size_of::<Bla>()) as u64,
+            usage: wgpu::BufferUsages::STORAGE | wgpu::BufferUsages::COPY_DST,
             mapped_at_creation: false,
         });
 
-        let bind_group_layout = device.create_bind_group_layout(&wgpu::BindGroupLayoutDescriptor {
-            label: Some("fractal 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: 1,
-                    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 bind_group_layout =
+            device.create_bind_group_layout(&fractal_bind_group_layout_desc());
 
-        let bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
-            label: Some("fractal bind group"),
-            layout: &bind_group_layout,
-            entries: &[
-                wgpu::BindGroupEntry {
-                    binding: 0,
-                    resource: uniform_buffer.as_entire_binding(),
-                },
-                wgpu::BindGroupEntry {
-                    binding: 1,
-                    resource: ref_buffer.as_entire_binding(),
-                },
-            ],
-        });
+        let bind_group = fractal_bind_group(
+            device,
+            &bind_group_layout,
+            &uniform_buffer,
+            &ref_buffer,
+            &bla_buffer,
+        );
 
         let pipeline_layout = device.create_pipeline_layout(&wgpu::PipelineLayoutDescriptor {
             label: Some("fractal pipeline layout"),
@@ -231,9 +205,8 @@ impl FractalRenderer {
             immediate_size: 0,
         });
 
-        // Iteration pass: perturbation iterate → data texture (color-independent).
-        let iterate_pipeline = device.create_render_pipeline(&wgpu::RenderPipelineDescriptor {
-            label: Some("fractal iterate pipeline"),
+        let pipeline = device.create_render_pipeline(&wgpu::RenderPipelineDescriptor {
+            label: Some("fractal pipeline"),
             layout: Some(&pipeline_layout),
             vertex: wgpu::VertexState {
                 module: &shader,
@@ -243,107 +216,6 @@ impl FractalRenderer {
             },
             fragment: Some(wgpu::FragmentState {
                 module: &shader,
-                entry_point: Some("fs_data"),
-                targets: &[Some(wgpu::ColorTargetState {
-                    format: DATA_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,
-        });
-
-        // Combined iterate + colour in one pass — for PNG export only.
-        let export_pipeline = device.create_render_pipeline(&wgpu::RenderPipelineDescriptor {
-            label: Some("fractal export pipeline"),
-            layout: Some(&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_color"),
-                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,
-        });
-
-        // Colourise pass: data texture + colour uniforms → colour texture.
-        let colorize_shader = device.create_shader_module(wgpu::ShaderModuleDescriptor {
-            label: Some("colorize"),
-            source: wgpu::ShaderSource::Wgsl(include_str!("../shaders/colorize.wgsl").into()),
-        });
-        let colorize_bind_group_layout =
-            device.create_bind_group_layout(&wgpu::BindGroupLayoutDescriptor {
-                label: Some("colorize 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: 1,
-                        visibility: wgpu::ShaderStages::FRAGMENT,
-                        ty: wgpu::BindingType::Texture {
-                            // Nearest only: iteration data must not be filtered.
-                            sample_type: wgpu::TextureSampleType::Float { filterable: false },
-                            view_dimension: wgpu::TextureViewDimension::D2,
-                            multisampled: false,
-                        },
-                        count: None,
-                    },
-                    wgpu::BindGroupLayoutEntry {
-                        binding: 2,
-                        visibility: wgpu::ShaderStages::FRAGMENT,
-                        ty: wgpu::BindingType::Buffer {
-                            ty: wgpu::BufferBindingType::Uniform,
-                            has_dynamic_offset: false,
-                            min_binding_size: None,
-                        },
-                        count: None,
-                    },
-                ],
-            });
-        let colorize_pipeline_layout =
-            device.create_pipeline_layout(&wgpu::PipelineLayoutDescriptor {
-                label: Some("colorize pipeline layout"),
-                bind_group_layouts: &[Some(&colorize_bind_group_layout)],
-                immediate_size: 0,
-            });
-        let colorize_pipeline = device.create_render_pipeline(&wgpu::RenderPipelineDescriptor {
-            label: Some("colorize pipeline"),
-            layout: Some(&colorize_pipeline_layout),
-            vertex: wgpu::VertexState {
-                module: &colorize_shader,
-                entry_point: Some("vs_main"),
-                buffers: &[],
-                compilation_options: Default::default(),
-            },
-            fragment: Some(wgpu::FragmentState {
-                module: &colorize_shader,
                 entry_point: Some("fs_main"),
                 targets: &[Some(wgpu::ColorTargetState {
                     format: target_format,
@@ -428,23 +300,19 @@ impl FractalRenderer {
         });
 
         Self {
-            iterate_pipeline,
-            export_pipeline,
+            pipeline,
             bind_group_layout,
             uniform_buffer,
             ref_buffer,
-            lights_buffer,
+            bla_buffer,
             bind_group,
             target_format,
             uploaded_generation: u64::MAX,
-            colorize_pipeline,
-            colorize_bind_group_layout,
             blit_pipeline,
             blit_bind_group_layout,
             blit_sampler,
             cache: None,
-            iterated: None,
-            colored: None,
+            rendered: None,
         }
     }
 
@@ -458,29 +326,13 @@ impl FractalRenderer {
             return;
         }
 
-        let extent = wgpu::Extent3d {
+        let texture = device.create_texture(&wgpu::TextureDescriptor {
+            label: Some("fractal cache"),
+            size: wgpu::Extent3d {
                 width,
                 height,
                 depth_or_array_layers: 1,
-        };
-
-        // Iteration-data texture (color-independent escape data).
-        let data_texture = device.create_texture(&wgpu::TextureDescriptor {
-            label: Some("fractal data"),
-            size: extent,
-            mip_level_count: 1,
-            sample_count: 1,
-            dimension: wgpu::TextureDimension::D2,
-            format: DATA_FORMAT,
-            usage: wgpu::TextureUsages::RENDER_ATTACHMENT | wgpu::TextureUsages::TEXTURE_BINDING,
-            view_formats: &[],
-        });
-        let data_view = data_texture.create_view(&wgpu::TextureViewDescriptor::default());
-
-        // Colour texture (colourise output; blit source).
-        let color_texture = device.create_texture(&wgpu::TextureDescriptor {
-            label: Some("fractal color cache"),
-            size: extent,
+            },
             mip_level_count: 1,
             sample_count: 1,
             dimension: wgpu::TextureDimension::D2,
@@ -488,26 +340,7 @@ impl FractalRenderer {
             usage: wgpu::TextureUsages::RENDER_ATTACHMENT | wgpu::TextureUsages::TEXTURE_BINDING,
             view_formats: &[],
         });
-        let color_view = color_texture.create_view(&wgpu::TextureViewDescriptor::default());
-
-        let colorize_bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
-            label: Some("colorize bind group"),
-            layout: &self.colorize_bind_group_layout,
-            entries: &[
-                wgpu::BindGroupEntry {
-                    binding: 0,
-                    resource: self.uniform_buffer.as_entire_binding(),
-                },
-                wgpu::BindGroupEntry {
-                    binding: 1,
-                    resource: wgpu::BindingResource::TextureView(&data_view),
-                },
-                wgpu::BindGroupEntry {
-                    binding: 2,
-                    resource: self.lights_buffer.as_entire_binding(),
-                },
-            ],
-        });
+        let view = texture.create_view(&wgpu::TextureViewDescriptor::default());
 
         let blit_bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
             label: Some("blit bind group"),
@@ -515,7 +348,7 @@ impl FractalRenderer {
             entries: &[
                 wgpu::BindGroupEntry {
                     binding: 0,
-                    resource: wgpu::BindingResource::TextureView(&color_view),
+                    resource: wgpu::BindingResource::TextureView(&view),
                 },
                 wgpu::BindGroupEntry {
                     binding: 1,
@@ -525,30 +358,21 @@ impl FractalRenderer {
         });
 
         self.cache = Some(CacheTarget {
-            data_view,
-            color_view,
-            colorize_bind_group,
+            view,
             blit_bind_group,
             width,
             height,
         });
-        // New textures → old renders are gone.
-        self.iterated = None;
-        self.colored = None;
+        // New texture → old render is gone.
+        self.rendered = None;
     }
 
     /// Handles needed to build a standalone [`ExportRender`] off the UI thread:
     /// the (immutable) pipeline and its bind-group layout, plus the target
     /// format. Cloned so the caller can drop the render-state lock before use.
-    pub fn export_handles(
-        &self,
-    ) -> (
-        wgpu::RenderPipeline,
-        wgpu::BindGroupLayout,
-        wgpu::TextureFormat,
-    ) {
+    pub fn export_handles(&self) -> (wgpu::RenderPipeline, wgpu::BindGroupLayout, wgpu::TextureFormat) {
         (
-            self.export_pipeline.clone(),
+            self.pipeline.clone(),
             self.bind_group_layout.clone(),
             self.target_format,
         )
@@ -588,6 +412,7 @@ impl ExportRender {
         height: u32,
         uniforms: Uniforms,
         reference: &[[f32; 2]],
+        bla: &[Bla],
     ) -> Self {
         let uniform_buffer = device.create_buffer(&wgpu::BufferDescriptor {
             label: Some("export uniforms"),
@@ -608,20 +433,24 @@ impl ExportRender {
             queue.write_buffer(&ref_buffer, 0, bytemuck::cast_slice(&reference[..count]));
         }
 
-        let bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
-            label: Some("export bind group"),
-            layout: bind_group_layout,
-            entries: &[
-                wgpu::BindGroupEntry {
-                    binding: 0,
-                    resource: uniform_buffer.as_entire_binding(),
-                },
-                wgpu::BindGroupEntry {
-                    binding: 1,
-                    resource: ref_buffer.as_entire_binding(),
-                },
-            ],
+        let bla_count = bla.len().min(MAX_BLA_ENTRIES);
+        let bla_buffer = device.create_buffer(&wgpu::BufferDescriptor {
+            label: Some("export bla table"),
+            size: (bla_count.max(1) * std::mem::size_of::<Bla>()) as u64,
+            usage: wgpu::BufferUsages::STORAGE | wgpu::BufferUsages::COPY_DST,
+            mapped_at_creation: false,
         });
+        if bla_count > 0 {
+            queue.write_buffer(&bla_buffer, 0, bytemuck::cast_slice(&bla[..bla_count]));
+        }
+
+        let bind_group = fractal_bind_group(
+            device,
+            bind_group_layout,
+            &uniform_buffer,
+            &ref_buffer,
+            &bla_buffer,
+        );
 
         let texture = device.create_texture(&wgpu::TextureDescriptor {
             label: Some("export target"),
@@ -757,59 +586,6 @@ impl ExportRender {
     }
 }
 
-/// Render `er` tile by tile (blocking on the GPU after each tile so progress
-/// reflects real work), read it back, and encode the result as PNG bytes.
-/// Blocks the calling thread throughout, so it's only for native targets:
-/// the UI export path runs it on a background thread, headless rendering
-/// runs it directly since it has no frame loop to share a thread with.
-#[cfg(not(target_arch = "wasm32"))]
-pub fn export_to_png_blocking(
-    device: &wgpu::Device,
-    queue: &wgpu::Queue,
-    er: &ExportRender,
-    mut on_progress: impl FnMut(&'static str, f32),
-) -> Vec<u8> {
-    // Progress budget: rendering fills [0, RENDER_END], encoding the rest.
-    const RENDER_END: f32 = 0.6;
-
-    for t in 0..er.tiles {
-        er.render_tile(device, queue, t);
-        let _ = device.poll(wgpu::PollType::Wait {
-            submission_index: None,
-            timeout: None,
-        });
-        let done = (t + 1) as f32 / er.tiles as f32;
-        on_progress("Rendering", RENDER_END * done);
-    }
-    er.copy_to_readback(device, queue);
-
-    let (tx, rx) = std::sync::mpsc::channel();
-    er.readback()
-        .slice(..)
-        .map_async(wgpu::MapMode::Read, move |res| {
-            let _ = tx.send(res);
-        });
-    let _ = device.poll(wgpu::PollType::Wait {
-        submission_index: None,
-        timeout: None,
-    });
-    let _ = rx.recv();
-
-    on_progress("Encoding", RENDER_END);
-    let png = {
-        let data = er
-            .readback()
-            .slice(..)
-            .get_mapped_range()
-            .expect("map readback buffer");
-        encode_png_with_progress(&data, er.width, er.height, er.padded_bpr, er.swap_rb, |f| {
-            on_progress("Encoding", RENDER_END + (0.97 - RENDER_END) * f)
-        })
-    };
-    er.readback().unmap();
-    png
-}
-
 /// Convert a padded BGRA/RGBA readback into tightly-packed RGBA8 and encode it
 /// as PNG bytes, reporting progress in `[0, 1]` via `on_progress` as rows are
 /// streamed to the compressor (encoding is the slow, subdividable phase).
@@ -858,13 +634,13 @@ pub fn encode_png_with_progress(
 
 /// A per-frame paint callback. Carries this frame's uniforms plus a reference to
 /// the current reference orbit (cheap `Arc` clone). The orbit is only re-uploaded
-/// when its `generation` changes; the expensive iteration pass re-runs only when
-/// a geometry input changes, and colour-only changes re-run just the cheap
-/// colourise pass (see `prepare`).
+/// to the GPU when its `generation` changes, and the fractal is only re-rendered
+/// into the cache when the uniforms, generation, or `size_px` change.
 pub struct FractalCallback {
     pub uniforms: Uniforms,
-    pub lights: Vec<Light>,
     pub reference: Arc<Vec<[f32; 2]>>,
+    /// BLA table for the current reference (empty when BLA is off/unsupported).
+    pub bla: Arc<Vec<Bla>>,
     pub generation: u64,
     /// Widget size in physical pixels — the cache texture resolution.
     pub size_px: [u32; 2],
@@ -894,47 +670,39 @@ impl egui_wgpu::CallbackTrait for FractalCallback {
                 0,
                 bytemuck::cast_slice(&self.reference[..count]),
             );
+            let bla_count = self.bla.len().min(MAX_BLA_ENTRIES);
+            if bla_count > 0 {
+                queue.write_buffer(
+                    &renderer.bla_buffer,
+                    0,
+                    bytemuck::cast_slice(&self.bla[..bla_count]),
+                );
+            }
             renderer.uploaded_generation = self.generation;
         }
 
-        // Iteration (expensive) re-runs only when the geometry inputs change;
-        // colourise (cheap) re-runs when it did, or when only a colour changed —
-        // so palette / colour-scale / offset tweaks (e.g. colour cycling) skip
-        // the perturbation entirely.
-        let iter_dirty = renderer.iterated.as_ref().is_none_or(|r| {
+        // Re-render the cache only when what it depends on changed.
+        let dirty = renderer.rendered.as_ref().is_none_or(|r| {
             r.generation != self.generation
                 || r.width != width
                 || r.height != height
-                || geom_differs(&r.uniforms, &self.uniforms)
+                || bytemuck::bytes_of(&r.uniforms) != bytemuck::bytes_of(&self.uniforms)
         });
-        let color_dirty = iter_dirty
-            || renderer.colored.as_ref().is_none_or(|c| {
-                c.width != width || c.height != height || color_differs(&c.uniforms, &self.uniforms)
-            })
-            || true;
-
-        if !color_dirty {
-            return Vec::new(); // cache still valid; paint() just blits it
+        if !dirty {
+            return Vec::new();
         }
 
-        // Both passes read the uniform buffer; refresh it once.
         queue.write_buffer(
             &renderer.uniform_buffer,
             0,
             bytemuck::bytes_of(&self.uniforms),
         );
-        let mut bytes = [0; size_of::<Light>() * MAX_LIGHT_COUNT];
-        bytes[..self.lights.len() * size_of::<Light>()]
-            .copy_from_slice(bytemuck::cast_slice(&self.lights));
-        queue.write_buffer(&renderer.lights_buffer, 0, &bytes);
 
         if let Some(cache) = &renderer.cache {
-            if iter_dirty {
-                // Iteration pass: perturbation iterate → data texture.
             let mut pass = egui_encoder.begin_render_pass(&wgpu::RenderPassDescriptor {
-                    label: Some("fractal iterate pass"),
+                label: Some("fractal cache pass"),
                 color_attachments: &[Some(wgpu::RenderPassColorAttachment {
-                        view: &cache.data_view,
+                    view: &cache.view,
                     depth_slice: None,
                     resolve_target: None,
                     ops: wgpu::Operations {
@@ -947,46 +715,17 @@ impl egui_wgpu::CallbackTrait for FractalCallback {
                 occlusion_query_set: None,
                 multiview_mask: None,
             });
-                pass.set_pipeline(&renderer.iterate_pipeline);
+            pass.set_pipeline(&renderer.pipeline);
             pass.set_bind_group(0, &renderer.bind_group, &[]);
             pass.draw(0..3, 0..1);
         }
 
-            // Colourise pass: data texture → colour texture.
-            let mut pass = egui_encoder.begin_render_pass(&wgpu::RenderPassDescriptor {
-                label: Some("fractal colorize pass"),
-                color_attachments: &[Some(wgpu::RenderPassColorAttachment {
-                    view: &cache.color_view,
-                    depth_slice: None,
-                    resolve_target: None,
-                    ops: wgpu::Operations {
-                        load: wgpu::LoadOp::Clear(wgpu::Color::BLACK),
-                        store: wgpu::StoreOp::Store,
-                    },
-                })],
-                depth_stencil_attachment: None,
-                timestamp_writes: None,
-                occlusion_query_set: None,
-                multiview_mask: None,
-            });
-            pass.set_pipeline(&renderer.colorize_pipeline);
-            pass.set_bind_group(0, &cache.colorize_bind_group, &[]);
-            pass.draw(0..3, 0..1);
-        }
-
-        if iter_dirty {
-            renderer.iterated = Some(IterState {
+        renderer.rendered = Some(RenderedState {
             uniforms: self.uniforms,
             generation: self.generation,
             width,
             height,
         });
-        }
-        renderer.colored = Some(ColorState {
-            uniforms: self.uniforms,
-            width,
-            height,
-        });
         Vec::new()
     }
 

src/fractal/share.rs

@@ -21,44 +21,28 @@ pub struct ShareState {
     pub half_height: f64,
     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),
     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={}", match self.kind {
             FractalKind::Mandelbrot => "mandel",
             FractalKind::BurningShip => "burning",
             FractalKind::Multibrot => "multi",
             FractalKind::Tricorn => "tricorn",
-                FractalKind::Celtic => "celtic",
-                FractalKind::Perpendicular => "perp",
-                FractalKind::Buffalo => "buffalo",
-                FractalKind::Phoenix => "phoenix",
-                FractalKind::Lambda => "lambda",
-            }
-        ));
+        }));
         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={}",
             self.color_scale, self.color_offset, self.palette
@@ -84,12 +68,7 @@ impl ShareState {
                     "multi" => FractalKind::Multibrot,
                     "burning" => FractalKind::BurningShip,
                     "tricorn" => FractalKind::Tricorn,
-                    "celtic" => FractalKind::Celtic,
-                    "perp" => FractalKind::Perpendicular,
-                    "buffalo" => FractalKind::Buffalo,
-                    "phoenix" => FractalKind::Phoenix,
-                    "lambda" => FractalKind::Lambda,
-                    _ => FractalKind::Mandelbrot,
+                    _ => FractalKind::Mandelbrot
                 })
                 .unwrap_or(FractalKind::Mandelbrot),
             power: map.get("pw").and_then(|s| s.parse().ok()).unwrap_or(2),
@@ -101,18 +80,9 @@ 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),
-            ),
             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),
         })
     }
 }
@@ -125,19 +95,16 @@ mod tests {
     fn round_trip() {
         let s = ShareState {
             julia: true,
-            kind: FractalKind::Phoenix,
+            kind: FractalKind::Multibrot,
             power: 5,
             center_re: "-0.743643887037158704752191506114774".into(),
             center_im: "0.131825904205311970493132056385139".into(),
             half_height: 1.5e-20,
             iterations: 4000,
             julia_c: (-0.123, 0.745),
-            phoenix_p: (-0.5, 0.1),
-            lambda_l: (-0.5, 0.0),
             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);
@@ -148,9 +115,7 @@ 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.palette, s.palette);
-        assert_eq!(d.shadow_palette, s.shadow_palette);
     }
 
     #[test]

src/headless.rs

@@ -1,82 +0,0 @@
-// 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.
-
-use eframe::egui_wgpu::wgpu;
-
-use crate::app::{FractalApp, unix_timestamp};
-use crate::cli::Cli;
-use crate::fractal::{ExportRender, FractalRenderer, export_to_png_blocking};
-
-/// Cap on the output image dimension (px), to stay within GPU texture limits.
-const MAX_DIM: u32 = 8192 * 16;
-
-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);
-    let export_path = cli
-        .export_path
-        .clone()
-        .unwrap_or_else(|| format!("fractal-{}.png", unix_timestamp()));
-
-    let mut app = FractalApp::default_state();
-    app.apply_cli(cli);
-
-    eprintln!("computing reference orbit…");
-    app.compute_reference_blocking();
-
-    let (device, queue) = pollster::block_on(request_device())?;
-    let format = wgpu::TextureFormat::Rgba8UnormSrgb;
-    let renderer = FractalRenderer::new(&device, format);
-    let (pipeline, bind_group_layout, format) = renderer.export_handles();
-
-    let uniforms = app.make_uniforms(width as f64 / height as f64);
-    let er = ExportRender::new(
-        &device,
-        &queue,
-        pipeline,
-        &bind_group_layout,
-        format,
-        width,
-        height,
-        uniforms,
-        app.reference_points(),
-    );
-
-    eprintln!("rendering {width}×{height}…");
-    let png = export_to_png_blocking(&device, &queue, &er, |phase, fraction| {
-        eprint!("\r{phase} {:>3.0}%", fraction * 100.0);
-    });
-    eprintln!();
-
-    std::fs::write(&export_path, &png).map_err(|e| format!("save failed: {e}"))?;
-    println!("saved {export_path} ({width}×{height})");
-    Ok(())
-}
-
-/// 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}"))
-}

src/lights.rs

@@ -1,55 +0,0 @@
-use std::f32::consts::PI;
-
-use bytemuck::{Pod, Zeroable};
-use egui::{Color32, 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 {
-    pub fn widget(&mut self, ui: &mut Ui) -> bool {
-        let formater = |v, _| format!("{}°", ((v as f32 * 180. / PI) as u32));
-        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)
-                    .speed(0.02),
-            );
-            ui.label("φ:");
-            ui.add(
-                egui::DragValue::new(&mut self.altitude)
-                    .range(0.0..=PI / 2.)
-                    .custom_formatter(formater)
-                    .speed(0.02),
-            );
-
-            del
-        })
-        .inner
-    }
-}

src/main.rs

@@ -1,7 +1,3 @@
-// Without these, rust fails to infer Send/Sync trait impls
-// Probably caused by the new trait solver
-#![recursion_limit = "256"]
-
 // Fractal Explorer — Rust + wgpu + egui + WGSL deep-zoom Mandelbrot.
 //
 // A single binary drives both native and web (WASM/WebGPU) builds; the two
@@ -10,13 +6,8 @@
 
 mod app;
 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;
 
@@ -34,12 +25,13 @@ fn wgpu_options() -> eframe::egui_wgpu::WgpuConfiguration {
 
     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| wgpu::DeviceDescriptor {
+        setup.device_descriptor = 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")]
         {
@@ -51,24 +43,11 @@ fn wgpu_options() -> eframe::egui_wgpu::WgpuConfiguration {
 
 #[cfg(not(target_arch = "wasm32"))]
 fn main() -> eframe::Result {
-    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);
-            }
-        };
-    }
-
     let native_options = eframe::NativeOptions {
         renderer: eframe::Renderer::Wgpu,
         wgpu_options: wgpu_options(),

src/shaders/buddhabrot.wgsl

@@ -1,299 +0,0 @@
-// 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 to a 16-byte multiple. 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,
-    _pad1: u32,
-    _pad2: u32,
-};
-
-const PALETTE_NEBULA: u32 = 0u;
-const PALETTE_YELLOW: u32 = 1u;
-const PALETTE_GRAYSCALE: u32 = 2u;
-
-const KIND_MANDELBROT: u32 = 0u;
-const KIND_BURNING_SHIP: u32 = 1u;
-const KIND_TRICORN: u32 = 2u;
-const KIND_MULTIBROT: u32 = 3u;
-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;
-
-@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 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);
-}
-
-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 u.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 u.kind == KIND_TRICORN {
-        return vec2<f32>(z.x * z.x - z.y * z.y, -2.0 * z.x * z.y) + c;
-    } else if u.kind == KIND_MULTIBROT {
-        return complex_pow(z, clamp(u.power, 2u, 8u)) + c;
-    } else if u.kind == KIND_CELTIC {
-        return vec2<f32>(abs(z.x * z.x - z.y * z.y), 2.0 * z.x * z.y) + c;
-    } else if u.kind == KIND_PERPENDICULAR {
-        return vec2<f32>(z.x * z.x - z.y * z.y, -2.0 * z.x * abs(z.y)) + c;
-    } else if u.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 u.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 u.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)));
-    }
-    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 u.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> {
-    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 vec4<f32>(verts[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

@@ -1,168 +0,0 @@
-// 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).
-
-// Must match `Uniforms` in mandelbrot.wgsl / the Rust `Uniforms` struct.
-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,
-    kind: u32,
-    power: u32,
-    dc_offset: vec2<f32>,
-    phoenix_p: vec2<f32>,
-    lambda_l: vec2<f32>,
-    de_coloring: u32,
-    shadow: u32,
-};
-
-struct Light {
-    azimuth: f32,
-    altitude: f32,
-    color: u32,
-    _pad: u32
-};
-
-@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>;
-
-// Smooth cyclic palettes (Inigo Quilez cosine palettes). Must match the palette
-// in mandelbrot.wgsl.
-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));
-}
-
-@vertex
-fn vs_main(@builtin(vertex_index) idx: u32) -> @builtin(position) vec4<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 vec4<f32>(verts[idx], 0.0, 1.0);
-}
-
-fn load(x: i32, y: i32) -> vec3<f32> {
-    let dist = textureLoad(data_tex, vec2<i32>(x, y), 0).g;
-    return vec3<f32>(f32(x), f32(y), dist);
-}
-
-fn compute_light(normal: vec3<f32>, light: vec3<f32>) -> vec3<f32> {
-    return vec3<f32>(max(0., dot(normal, normalize(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));
-}
-
-@fragment
-fn fs_main(@builtin(position) pos: vec4<f32>) -> @location(0) vec4<f32> {
-    if u.shadow != 0u {
-        if textureLoad(data_tex, vec2<i32>(i32(pos.x), i32(pos.y)), 0).b != 0. {
-            return vec4<f32>(0.1, 0.1, 0.1, 1.0);
-        } else {
-            let d = array<vec3<f32>, 3>(load(i32(pos.x), i32(pos.y)), load(i32(pos.x + 1), i32(pos.y)), load(i32(pos.x), i32(pos.y + 1)));
-
-            let normal = normalize(cross(d[1] - d[0], d[2] - d[0]));
-
-            var color: vec3<f32>;
-            if u.shadow_palette_id == 0u {
-                color = compute_light(normal,vec3<f32>(.5, .5, .5)) + 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., .5, .5)) * vec3<f32>(1., 0.5, 0.5) + compute_light(normal, vec3<f32>(0.5, 0., .5)) * vec3<f32>(0.5, 1., 1.);
-
-                color = filmic(color, 4.2);
-            } else {
-                color = vec3<f32>(0);
-                var light_count = 0;
-                for (var i = 0u ; i < 16; i++) {
-                    let light_color = unpack4x8unorm(lights[i].color);
-                    if any(light_color != vec4<f32>(0)) {
-                        light_count       += 1;
-                    }
-
-                    color       += compute_light(normal, vec3<f32>(
-                        cos(lights[i].azimuth) * cos(lights[i].altitude),
-                        sin(lights[i].azimuth) * cos(lights[i].altitude),
-                        sin(lights[i].altitude))) * light_color.xyz * light_color.a;
-                }
-
-                color = filmic(color, 1. + f32(light_count));
-            }
-
-            return vec4<f32>(color, 1.0);
-        }
-    } 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;
-
-        let t = fract(ci * u.color_scale + u.color_offset);
-        var col = palette(u.palette_id, t) * 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);
-    }
-}

src/shaders/mandelbrot.wgsl

@@ -21,37 +21,37 @@ struct Uniforms {
     bailout_sq: f32,
     is_julia: u32,
     palette_id: u32,
-    shadow_palette_id: u32,
     aa_level: u32,
-    // Iteration formula (see the KIND_* constants below).
+    // Iteration formula: 0 Mandelbrot, 1 Burning Ship, 2 Tricorn, 3 Multibrot.
     kind: u32,
     // Exponent for the Multibrot kind.
     power: 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>,
     // 0 = escape-time coloring, 1 = distance-estimation shading.
     de_coloring: u32,
-    // 0 = classic colors, 1 = shadows
-    shadow: u32,
+    // 0 = per-iteration stepping, 1 = BLA iteration-skipping (square map only).
+    use_bla: u32,
+};
+
+// One merged linear step from the BLA table: e_{n+l} = A e + B dc, valid while
+// |e| < r. Matches the Rust `Bla` struct (24-byte std430 stride).
+struct Bla {
+    a: vec2<f32>,
+    b: vec2<f32>,
+    r: f32,
+    l: u32,
 };
 
 const KIND_MANDELBROT: u32 = 0u;
 const KIND_BURNING_SHIP: u32 = 1u;
 const KIND_TRICORN: u32 = 2u;
 const KIND_MULTIBROT: u32 = 3u;
-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;
 
 @group(0) @binding(0) var<uniform> u: Uniforms;
 @group(0) @binding(1) var<storage, read> ref_orbit: array<vec2<f32>>;
+// BLA table, levels concatenated (level 0 first). Per-level counts are recomputed
+// from `ref_len` exactly as the CPU builder laid them out.
+@group(0) @binding(2) var<storage, read> bla_table: array<Bla>;
 
 struct VsOut {
     @builtin(position) pos: vec4<f32>,
@@ -89,7 +89,7 @@ fn conj(a: vec2<f32>) -> vec2<f32> {
 // the sign flips that happen all along the axes, where the ship's detail lives.
 fn diffabs(c: f32, d: f32) -> f32 {
     let cd = c + d;
-    if c >= 0.0 {
+    if (c >= 0.0) {
         return select(-(2.0 * c + d), d, cd >= 0.0);
     }
     return select(-d, 2.0 * c + d, cd > 0.0);
@@ -127,7 +127,7 @@ fn multibrot_delta(z: vec2<f32>, e: vec2<f32>, p: u32) -> vec2<f32> {
 // where `z` is the reference orbit value X_m. `step_add` (dc) is added by the
 // caller. Must match `FractalKind` on the CPU side.
 fn advance_delta(z: vec2<f32>, e: vec2<f32>) -> vec2<f32> {
-    if u.kind == KIND_BURNING_SHIP {
+    if (u.kind == KIND_BURNING_SHIP) {
         // (|x| + i|y|)^2 has real part x^2 - y^2 (an ordinary square delta) and
         // imaginary part 2|x y|. The imaginary delta is 2(|x y| - |X Y|); diffabs
         // computes it exactly, even where the product x y changes sign — which the
@@ -136,35 +136,14 @@ fn advance_delta(z: vec2<f32>, e: vec2<f32>) -> vec2<f32> {
         let base = 2.0 * cmul(z, e) + cmul(e, e);
         let dp = z.x * e.y + z.y * e.x + e.x * e.y;
         return vec2<f32>(base.x, 2.0 * diffabs(z.x * z.y, dp));
-    } else if u.kind == KIND_TRICORN {
+    } else if (u.kind == KIND_TRICORN) {
         let cz = conj(z);
         let ce = conj(e);
         return 2.0 * cmul(cz, ce) + cmul(ce, ce);
-    } else if u.kind == KIND_MULTIBROT {
+    } else if (u.kind == KIND_MULTIBROT) {
         return multibrot_delta(z, e, clamp(u.power, 2u, 8u));
-    } else if u.kind == KIND_CELTIC {
-        // z^2 delta split: sq.x = delta of Re(z^2), sq.y = delta of Im(z^2).
-        // Celtic abs the real output, so |Re(z^2)| delta = diffabs(Re(Z^2), sq.x).
-        let sq = 2.0 * cmul(z, e) + cmul(e, e);
-        return vec2<f32>(diffabs(z.x * z.x - z.y * z.y, sq.x), sq.y);
-    } else if u.kind == KIND_BUFFALO {
-        // Abs both outputs: real |Re(z^2)|, imag -|Im(z^2)| (Im(Z^2) = 2 X Y).
-        let sq = 2.0 * cmul(z, e) + cmul(e, e);
-        return vec2<f32>(diffabs(z.x * z.x - z.y * z.y, sq.x),
-                         -diffabs(2.0 * z.x * z.y, sq.y));
-    } else if u.kind == KIND_PERPENDICULAR {
-        // real x^2 - y^2 (ordinary square delta), imag -2 x |y|.
-        // d(-2 x |y|) = -2[ X·(|Y+ey|-|Y|) + ex·|Y+ey| ]; diffabs gives |Y+ey|-|Y|.
-        let sq = 2.0 * cmul(z, e) + cmul(e, e);
-        let da = diffabs(z.y, e.y);        // |Y + ey| - |Y|
-        let abs_yf = abs(z.y) + da;        // |Y + ey|
-        return vec2<f32>(sq.x, -2.0 * (z.x * da + e.x * abs_yf));
-    } else if u.kind == KIND_LAMBDA {
-        // Lambda map: z^{n+1} = λ·z·(1-z). Delta: e = λ·e·(1-2z-e).
-        let one_minus_2z_minus_e = vec2<f32>(1.0 - 2.0 * z.x - e.x, -2.0 * z.y - e.y);
-        return cmul(u.lambda_l, cmul(e, one_minus_2z_minus_e));
     }
-    return 2.0 * cmul(z, e) + cmul(e, e); // Mandelbrot (and Phoenix square part)
+    return 2.0 * cmul(z, e) + cmul(e, e); // Mandelbrot
 }
 
 // Derivative f'(Z) of the iteration map at the full value Z, used to propagate
@@ -173,55 +152,82 @@ fn advance_delta(z: vec2<f32>, e: vec2<f32>) -> vec2<f32> {
 // Burning Ship / Tricorn we use |f'| ~ |2Z|, which keeps the DE magnitude close
 // enough to de-speckle filaments.
 fn fprime(z: vec2<f32>) -> vec2<f32> {
-    if u.kind == KIND_MULTIBROT {
+    if (u.kind == KIND_MULTIBROT) {
         let p = clamp(u.power, 2u, 8u);
         var zk = vec2<f32>(1.0, 0.0); // Z^0
         for (var k: u32 = 1u; k < p; k = k + 1u) {
             zk = cmul(zk, z); // -> Z^{p-1}
         }
         return f32(p) * zk;
-    } else if u.kind == KIND_LAMBDA {
-        // Lambda: f'(z) = λ·(1-2z).
-        return cmul(u.lambda_l, vec2<f32>(1.0 - 2.0 * z.x, -2.0 * z.y));
     }
     return 2.0 * z;
 }
 
 // Smooth cyclic palettes (Inigo Quilez cosine palettes), selected by id.
 fn palette(id: u32, t: f32) -> vec3<f32> {
-    if id == 4u {
+    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 {
+    if (id == 1u) {
         d = vec3<f32>(0.00, 0.33, 0.67); // rainbow
-    } else if id == 2u {
+    } else if (id == 2u) {
         d = vec3<f32>(0.30, 0.20, 0.20); // warm ember
-    } else if id == 3u {
+    } 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));
 }
 
-// Escape data for one sample: `ci` is the (color-independent) palette parameter,
-// `de` the distance-estimate darkening factor in [0,1], `escaped` false for the
-// interior of the set. Splitting iteration from coloring lets a colour change be
-// remapped cheaply (see the colourise pass) without re-iterating.
-struct Sample {
-    ci: f32,
-    de: f32,
-    escaped: bool,
+// Result of a BLA lookup at an orbit index.
+struct Hop {
+    found: bool,
+    a: vec2<f32>,
+    b: vec2<f32>,
+    l: u32,
 };
 
-// Perturbation iterate a single sample. `offset` is the per-pixel offset in
-// complex units. For Mandelbrot it is the c-plane offset added every step (delta
-// starts at 0); for Julia it is the z-plane offset that seeds the initial delta
-// (c is fixed, so nothing is added per step).
-fn iterate_sample(offset: vec2<f32>, px: f32) -> Sample {
+// Longest valid BLA skip starting at orbit index `n` for a delta of squared
+// magnitude `emag2`. Walks levels low->high, recomputing each level's flat-array
+// start and count from `ref_len` (count[0] = ref_len-1, halving each level).
+// Radii shrink with level and alignment is monotonic, so the valid levels form a
+// prefix: we keep the last valid one and stop at the first that fails.
+fn bla_find(n: u32, emag2: f32) -> Hop {
+    var res: Hop;
+    res.found = false;
+
+    var start: u32 = 0u;
+    var count: u32 = u.ref_len - 1u;
+    var lv: u32 = 0u;
+    loop {
+        if (count == 0u) { break; }
+        let step = 1u << lv;
+        if ((n & (step - 1u)) != 0u) { break; } // n not aligned to this level
+        let idx = n >> lv;
+        if (idx >= count) { break; }            // run would exceed the orbit
+        let b = bla_table[start + idx];
+        if (emag2 >= b.r * b.r) { break; }       // delta too large: not valid
+        res.found = true;
+        res.a = b.a;
+        res.b = b.b;
+        res.l = b.l;
+        start = start + count;
+        count = count / 2u;
+        lv = lv + 1u;
+    }
+    return res;
+}
+
+// Perturbation iterate + color a single sample. `offset` is the per-pixel
+// offset in complex units. For Mandelbrot it is the c-plane offset added every
+// step (delta starts at 0); for Julia it is the z-plane offset that seeds the
+// initial delta (c is fixed, so nothing is added per step). Interior pixels
+// return black.
+fn shade(offset: vec2<f32>, px: f32) -> vec3<f32> {
     let z0 = ref_orbit[0]; // reference start (0 for Mandelbrot, center for Julia)
 
     var step_add = offset;
@@ -230,11 +236,7 @@ fn iterate_sample(offset: vec2<f32>, px: f32) -> Sample {
     // (starts at 0, gains +1 each step); for Julia it is d/dz0 (starts at 1).
     var dz = vec2<f32>(0.0, 0.0);
     var dz_seed = vec2<f32>(1.0, 0.0);
-    // Previous-iterate state for the Phoenix two-term recurrence (delta of
-    // y_{n-1}, and its derivative for DE). Both start at 0 (y_{-1} = 0).
-    var e_prev = vec2<f32>(0.0, 0.0);
-    var dz_prev = vec2<f32>(0.0, 0.0);
-    if u.is_julia != 0u {
+    if (u.is_julia != 0u) {
         step_add = vec2<f32>(0.0, 0.0);
         e = offset;
         dz = vec2<f32>(1.0, 0.0);
@@ -251,39 +253,45 @@ fn iterate_sample(offset: vec2<f32>, px: f32) -> Sample {
         z = xm + e;
 
         let z2 = dot(z, z);
-            if z2 > u.bailout_sq {
+        if (z2 > u.bailout_sq) {
             escaped = true;
             break;
         }
-            if n >= u.max_iter {
+        if (n >= u.max_iter) {
             break; // interior
         }
 
+        // Advance one step, or skip a whole run via BLA when the delta is small
+        // enough (square map only; other kinds keep `use_bla == 0`). The orbit
+        // derivative for DE follows the same linear map: over a run it advances
+        // by the run's own (A, B) coefficients, matching the per-step recurrence.
+        var did_skip = false;
+        if (u.use_bla != 0u) {
+            let hop = bla_find(m, dot(e, e));
+            if (hop.found) {
+                if (u.de_coloring != 0u) {
+                    dz = cmul(hop.a, dz) + cmul(hop.b, dz_seed);
+                }
+                e = cmul(hop.a, e) + cmul(hop.b, step_add);
+                m = m + hop.l;
+                n = n + hop.l;
+                did_skip = true;
+            }
+        }
+        if (!did_skip) {
             // Propagate the derivative of the full orbit (unaffected by rebasing,
             // which only re-expresses the same value). Only when DE is enabled.
-        // Phoenix's two-term map adds p·dz_{n-1} and carries the previous dz.
-            if u.de_coloring != 0u {
-                var dz_new = cmul(fprime(z), dz) + dz_seed;
-                if u.kind == KIND_PHOENIX {
-                    dz_new = dz_new + cmul(u.phoenix_p, dz_prev);
-                    dz_prev = dz;
+            if (u.de_coloring != 0u) {
+                dz = cmul(fprime(z), dz) + dz_seed;
             }
-                dz = dz_new;
-            }
-
             // Advance the delta by this fractal's formula (+ dc for the set plane).
-        // Phoenix additionally adds p·e_{n-1} and carries the previous delta.
-            let e_old = e;
             e = advance_delta(xm, e) + step_add;
-            if u.kind == KIND_PHOENIX {
-                e = e + cmul(u.phoenix_p, e_prev);
-                e_prev = e_old;
-            }
             m = m + 1u;
             n = n + 1u;
+        }
 
         // Keep the reference index valid and the delta small.
-            if m >= u.ref_len {
+        if (m >= u.ref_len) {
             // Reference exhausted: any pixel that followed it this far has
             // effectively escaped (interior pixels rebase before reaching here).
             z = ref_orbit[u.ref_len - 1u] + e;
@@ -291,21 +299,16 @@ fn iterate_sample(offset: vec2<f32>, px: f32) -> Sample {
             break;
         }
         let y = ref_orbit[m] + e;
-            if dot(y, y) < dot(e, e) {
+        if (dot(y, y) < dot(e, e)) {
             // Rebase to index 0: carry the full value as the new delta. Valid
             // because y_n = X[0] + (y_n - X[0]); for Mandelbrot X[0]=0.
-            // Phoenix: after rebasing the implied previous reference is Y[-1]=0,
-            // so the previous delta becomes the full previous value y_n (= z).
-                if u.kind == KIND_PHOENIX {
-                    e_prev = z;
-                }
             e = y - z0;
             m = 0u;
         }
     }
 
-    if !escaped {
-        return Sample(0.0, 1.0, false); // interior of the set
+    if (!escaped) {
+        return vec3<f32>(0.0, 0.0, 0.0); // interior of the set
     }
 
     let z2 = dot(z, z);
@@ -318,9 +321,10 @@ fn iterate_sample(offset: vec2<f32>, px: f32) -> Sample {
     // sqrt compresses the huge iteration counts of deep zooms so the palette
     // varies smoothly instead of aliasing into speckle.
     let ci = sqrt(max(smooth_i, 0.0));
+    let t = fract(ci * u.color_scale + u.color_offset);
+    var col = palette(u.palette_id, t);
 
-    var de = 1.0;
-    if u.de_coloring != 0u {
+    if (u.de_coloring != 0u) {
         // Exterior distance estimate (complex-plane units): |z|·ln|z| / |dz|.
         // Divided by the pixel footprint it becomes a distance in pixels; we
         // darken toward the boundary (< ~1 px away) so filaments stay crisp
@@ -328,81 +332,37 @@ fn iterate_sample(offset: vec2<f32>, px: f32) -> Sample {
         // boundary simply reads as dark, which is the correct limit.
         let zmag = sqrt(max(z2, 1.0));
         let dzmag = sqrt(max(dot(dz, dz), 1e-20));
-        let d = zmag * log(zmag) / dzmag;
-        var max_de = 1.;
-        if u.shadow != 0u {
-            max_de = 1000.;
+        let de = zmag * log(zmag) / dzmag;
+        let de_px = de / max(px, 1e-30);
+        col = col * clamp(de_px, 0.0, 1.0);
     }
-        de = clamp(d / max(px, 1e-30), 0.0, max_de);
-    }
-    return Sample(ci, de, true);
+    return col;
 }
 
-// Map a sample's escape data through the palette (+ DE darkening). This is the
-// only color-dependent step, so it can be redone without re-iterating. Interior
-// samples are black.
-fn color_sample(s: Sample) -> vec3<f32> {
-    if !s.escaped {
-        return vec3<f32>(0.0, 0.0, 0.0);
-    }
-    let t = fract(s.ci * u.color_scale + u.color_offset);
-    return palette(u.palette_id, t) * s.de;
-}
-
-// Iteration pass: write per-pixel escape data (color-independent) so a colour
-// change is remapped by the cheap colourise pass without re-iterating.
-//   R = ci (palette parameter), G = DE factor, B = interior fraction (for AA).
-// AA is grid-supersampled here; the interior fraction lets the colourise pass
-// anti-alias the set boundary (blend toward black) after the fact.
 @fragment
-fn fs_data(in: VsOut) -> @location(0) vec4<f32> {
+fn fs_main(in: VsOut) -> @location(0) vec4<f32> {
     let base = in.centered * u.span + u.dc_offset;
+
+    // Screen-space complex-units-per-pixel. Derivatives must be evaluated in
+    // uniform control flow, so take them here; used to place sub-pixel AA
+    // samples and to convert the distance estimate into pixels.
     let dx = dpdx(base);
     let dy = dpdy(base);
-    let px = length(abs(dx) + abs(dy));
+    let px = length(abs(dx) + abs(dy)); // ~ complex units per pixel (footprint)
 
     let aa = max(u.aa_level, 1u);
-    let inv = 1.0 / f32(aa);
-    var ci_sum = 0.0;
-    var de_sum = 0.0;
-    var escaped_n = 0u;
-    for (var sy: u32 = 0u; sy < aa; sy = sy + 1u) {
-        for (var sx: u32 = 0u; sx < aa; sx = sx + 1u) {
-            let jx = (f32(sx) + 0.5) * inv - 0.5;
-            let jy = (f32(sy) + 0.5) * inv - 0.5;
-            let s = iterate_sample(base + jx * dx + jy * dy, px);
-            if s.escaped {
-                ci_sum = ci_sum + s.ci;
-                de_sum = de_sum + s.de;
-                escaped_n = escaped_n + 1u;
-            }
-        }
-    }
-    let total = f32(aa * aa);
-    let ci_avg = select(0.0, ci_sum / f32(escaped_n), escaped_n > 0u);
-    let de_avg = select(1.0, de_sum / f32(escaped_n), escaped_n > 0u);
-    let interior_frac = 1.0 - f32(escaped_n) / total;
-    return vec4<f32>(ci_avg, de_avg, interior_frac, 1.0);
+    if (aa <= 1u) {
+        return vec4<f32>(shade(base, px), 1.0);
     }
 
-// Combined iterate + colour in a single pass, for PNG export (which never needs
-// incremental recolouring). The interactive path uses fs_data + the colourise
-// pass so colour changes skip iteration.
-@fragment
-fn fs_color(in: VsOut) -> @location(0) vec4<f32> {
-    let base = in.centered * u.span + u.dc_offset;
-    let dx = dpdx(base);
-    let dy = dpdy(base);
-    let px = length(abs(dx) + abs(dy));
-
-    let aa = max(u.aa_level, 1u);
-    let inv = 1.0 / f32(aa);
     var acc = vec3<f32>(0.0, 0.0, 0.0);
+    let inv = 1.0 / f32(aa);
     for (var sy: u32 = 0u; sy < aa; sy = sy + 1u) {
         for (var sx: u32 = 0u; sx < aa; sx = sx + 1u) {
+            // Sample centers evenly spread across the pixel, jitter in (-0.5, 0.5).
             let jx = (f32(sx) + 0.5) * inv - 0.5;
             let jy = (f32(sy) + 0.5) * inv - 0.5;
-            acc = acc + color_sample(iterate_sample(base + jx * dx + jy * dy, px));
+            acc = acc + shade(base + jx * dx + jy * dy, px);
         }
     }
     return vec4<f32>(acc / f32(aa * aa), 1.0);

src/view.rs

@@ -82,7 +82,7 @@ impl ViewState {
         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_im = &self.center_im - &big_from_f64(dy * cpp, bits);
+        self.center_im = &self.center_im - &big_from_f64(dy * cpp, bits); // y-down -> imag-up
     }
 
     /// Zoom by `factor` (<1 zooms in) keeping the complex point currently under
@@ -97,7 +97,7 @@ impl ViewState {
         // off * cpp * (1 - factor). (Derivation: new_c = fixed + (c-fixed)*f.)
         let k = cpp * (1.0 - factor);
         self.center_re = &self.center_re + &big_from_f64(off_x * k, bits);
-        self.center_im = &self.center_im + &big_from_f64(off_y * k, bits);
+        self.center_im = &self.center_im + &big_from_f64(off_y * k, bits); // y flip
         self.half_height *= factor;
     }
 

src/worker.rs

@@ -9,7 +9,7 @@
 use std::sync::mpsc::{Receiver, Sender, TryRecvError, channel};
 use std::thread;
 
-use crate::fractal::{FractalKind, compute_reference, compute_set_reference};
+use crate::fractal::{Bla, FractalKind, build_bla_table, compute_reference, compute_set_reference};
 use crate::view::{Big, big_from_f64};
 
 pub struct RefRequest {
@@ -22,10 +22,10 @@ pub struct RefRequest {
     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),
+    /// Build the BLA iteration-skip table for this orbit (square map only).
+    pub build_bla: bool,
+    /// Upper bound on any pixel's `|dc|`, sizing the BLA merge radii.
+    pub dc_max: f64,
 }
 
 pub struct RefResult {
@@ -33,6 +33,7 @@ pub struct RefResult {
     pub center_im: Big,
     pub half_height: f64,
     pub points: Vec<[f32; 2]>,
+    pub bla: Vec<Bla>,
 }
 
 pub struct RefWorker {
@@ -60,12 +61,18 @@ impl RefWorker {
                     }
 
                     let points = compute(&req);
+                    let bla = if req.build_bla {
+                        build_bla_table(&points, req.dc_max)
+                    } else {
+                        Vec::new()
+                    };
                     if res_tx
                         .send(RefResult {
                             center_re: req.center_re,
                             center_im: req.center_im,
                             half_height: req.half_height,
                             points,
+                            bla,
                         })
                         .is_err()
                     {
@@ -105,8 +112,6 @@ fn compute(req: &RefRequest) -> Vec<[f32; 2]> {
             req.precision,
             req.kind,
             req.power,
-            req.phoenix_p,
-            req.lambda_l,
         )
     } else {
         compute_set_reference(
@@ -116,8 +121,6 @@ fn compute(req: &RefRequest) -> Vec<[f32; 2]> {
             req.precision,
             req.kind,
             req.power,
-            req.phoenix_p,
-            req.lambda_l,
         )
     }
 }

tests/shader_valid.rs

@@ -25,20 +25,7 @@ fn mandelbrot_shader_is_valid() {
     );
 }
 
-#[test]
-fn colorize_shader_is_valid() {
-    validate("colorize.wgsl", include_str!("../src/shaders/colorize.wgsl"));
-}
-
 #[test]
 fn blit_shader_is_valid() {
     validate("blit.wgsl", include_str!("../src/shaders/blit.wgsl"));
 }
-
-#[test]
-fn buddhabrot_shader_is_valid() {
-    validate(
-        "buddhabrot.wgsl",
-        include_str!("../src/shaders/buddhabrot.wgsl"),
-    );
-}