feat: add shadow coloring

Cargo.toml

@@ -8,7 +8,6 @@ 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"
 
@@ -16,6 +15,7 @@ png = "0.18.1"
 env_logger = "0.11.11"
 
 [target.'cfg(target_arch = "wasm32")'.dependencies]
+futures-channel = { version = "0.3.34", default-features = false, features = ["alloc", "std"] }
 console_error_panic_hook = "0.1.7"
 console_log = "1.1.0"
 js-sys = "0.3.105"
@@ -26,6 +26,8 @@ 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

@@ -20,6 +20,7 @@ wasm-bindgen \
     target/wasm32-unknown-unknown/release/mandelbrot.wasm
 
 cp index.html "$OUT/index.html"
+cp favicon.ico "$OUT/favicon.ico"
 
 echo "==> done: $OUT/ (index.html, mandelbrot.js, mandelbrot_bg.wasm)"
 echo "    serve:  python3 -m http.server -d $OUT 8080"

src/fractal/buddhabrot.rs

@@ -0,0 +1,379 @@
+//! 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

@@ -1,11 +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 reference::{Bla, FractalKind, build_bla_table, compute_reference, compute_set_reference};
+pub use buddhabrot::{BuddhabrotCallback, BuddhabrotRenderer, BuddhabrotUniforms};
+pub use reference::{FractalKind, compute_reference, compute_set_reference};
 pub use renderer::{
     ExportRender, FractalCallback, FractalRenderer, MAX_REF_POINTS, Uniforms,
     encode_png_with_progress,

src/fractal/reference.rs

@@ -10,32 +10,31 @@
 //! * 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;
+use crate::view::{Big, big_from_f64};
 
 /// 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,
+    Mandelbrot = 0,
     /// `z -> (|Re z| + i|Im z|)^2 + c`.
-    BurningShip,
+    BurningShip = 1,
     /// `z -> conj(z)^2 + c` (the Mandelbar).
-    Tricorn,
+    Tricorn = 2,
     /// `z -> z^power + c` (power >= 2).
-    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,
-        }
-    }
+    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,
 }
 
 /// Reference orbit escapes once |Z|^2 exceeds this. Kept larger than the pixel
@@ -46,6 +45,7 @@ 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,
@@ -55,12 +55,23 @@ 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);
 
@@ -97,8 +108,45 @@ 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();
     }
@@ -132,6 +180,7 @@ 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,
@@ -139,157 +188,15 @@ 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,
+        &zero, &zero, center_re, center_im, max_iter, precision, kind, power, phoenix_p, lambda_l,
     )
 }
 
-// ---------------------------------------------------------------------------
-// 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::*;
@@ -300,7 +207,16 @@ 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);
+        let points = compute_set_reference(
+            &cr,
+            &ci,
+            60,
+            200,
+            FractalKind::Mandelbrot,
+            2,
+            (0.0, 0.0),
+            (0.0, 0.0),
+        );
 
         // Independent naive f64 orbit.
         let (c_re, c_im) = (-0.75_f64, 0.1_f64);
@@ -310,8 +226,14 @@ 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;
@@ -324,7 +246,16 @@ 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);
+        let points = compute_set_reference(
+            &cr,
+            &ci,
+            500,
+            120,
+            FractalKind::Mandelbrot,
+            2,
+            (0.0, 0.0),
+            (0.0, 0.0),
+        );
         assert_eq!(points.len(), 501, "interior orbit should not escape");
     }
 
@@ -333,7 +264,16 @@ 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);
+        let points = compute_set_reference(
+            &cr,
+            &ci,
+            60,
+            200,
+            FractalKind::BurningShip,
+            2,
+            (0.0, 0.0),
+            (0.0, 0.0),
+        );
 
         let (c_re, c_im) = (-1.75_f64, -0.03_f64);
         let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -353,7 +293,16 @@ 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);
+        let points = compute_set_reference(
+            &cr,
+            &ci,
+            60,
+            200,
+            FractalKind::Multibrot,
+            3,
+            (0.0, 0.0),
+            (0.0, 0.0),
+        );
 
         let (c_re, c_im) = (0.3_f64, 0.2_f64);
         let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -386,6 +335,8 @@ 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);
@@ -401,125 +352,121 @@ mod tests {
         }
     }
 
-    /// 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).
+    /// Celtic reference matches a naive f64 iteration: real = |x^2 - y^2| + cr.
     #[test]
-    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 points = compute_set_reference(&cr, &ci, 800, 160, FractalKind::Mandelbrot, 2);
-        assert!(points.len() > 64, "need a long orbit to exercise BLA levels");
-
-        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 = [
+    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),
-            (0.6e-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;
+            (0.0, 0.0),
+        );
 
-            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})"
-            );
+        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();
+        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 (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;
         }
-        assert!(any_skip, "BLA never took a multi-step skip — test is not exercising it");
     }
 }

src/fractal/renderer.rs

@@ -13,79 +13,40 @@ use std::sync::Arc;
 
 use eframe::egui_wgpu::{self, wgpu};
 
-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;
 
-/// 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;
+/// 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;
 
-/// 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 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
 }
 
-/// 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(),
-            },
-        ],
-    })
+/// 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 != b.shadow
 }
 
 /// GPU-side view + coloring parameters. Layout must match `Uniforms` in the
@@ -114,50 +75,79 @@ pub struct Uniforms {
     /// 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 = 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,
+    // 0 = classic colors, 1 = shadows
+    pub shadow: u32,
 }
 
-/// Offscreen texture the fractal is rendered into, plus the bind group used to
-/// blit it. Recreated whenever the widget's pixel size changes.
+/// 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.
 struct CacheTarget {
-    view: wgpu::TextureView,
+    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.
     blit_bind_group: wgpu::BindGroup,
     width: u32,
     height: u32,
 }
 
-/// 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 {
+/// 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 {
     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 {
-    pipeline: wgpu::RenderPipeline,
+    /// 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,
     bind_group_layout: wgpu::BindGroupLayout,
     uniform_buffer: wgpu::Buffer,
     ref_buffer: wgpu::Buffer,
-    bla_buffer: wgpu::Buffer,
     bind_group: wgpu::BindGroup,
     target_format: wgpu::TextureFormat,
-    /// Generation of the reference orbit + BLA table currently uploaded.
+    /// Generation of the reference orbit currently uploaded to `ref_buffer`.
     uploaded_generation: u64,
 
-    /// Blit pipeline + resources that copy the cache texture to egui's surface.
+    /// 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: wgpu::RenderPipeline,
     blit_bind_group_layout: wgpu::BindGroupLayout,
     blit_sampler: wgpu::Sampler,
-    /// The offscreen cache; `None` until the first frame sizes it.
+    /// The offscreen textures; `None` until the first frame sizes them.
     cache: Option<CacheTarget>,
-    /// What the cache currently holds; `None` forces a re-render.
-    rendered: Option<RenderedState>,
+    /// What the data texture holds; `None` forces re-iteration.
+    iterated: Option<IterState>,
+    /// What the colour texture holds; `None` forces a recolour.
+    colored: Option<ColorState>,
 }
 
 impl FractalRenderer {
@@ -181,23 +171,46 @@ impl FractalRenderer {
             mapped_at_creation: false,
         });
 
-        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 = fractal_bind_group(
-            device,
-            &bind_group_layout,
-            &uniform_buffer,
-            &ref_buffer,
-            &bla_buffer,
-        );
+        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 pipeline_layout = device.create_pipeline_layout(&wgpu::PipelineLayoutDescriptor {
             label: Some("fractal pipeline layout"),
@@ -205,8 +218,9 @@ impl FractalRenderer {
             immediate_size: 0,
         });
 
-        let pipeline = device.create_render_pipeline(&wgpu::RenderPipelineDescriptor {
-            label: Some("fractal pipeline"),
+        // Iteration pass: perturbation iterate → data texture (color-independent).
+        let iterate_pipeline = device.create_render_pipeline(&wgpu::RenderPipelineDescriptor {
+            label: Some("fractal iterate pipeline"),
             layout: Some(&pipeline_layout),
             vertex: wgpu::VertexState {
                 module: &shader,
@@ -216,6 +230,97 @@ 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,
+                    },
+                ],
+            });
+        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,
@@ -300,19 +405,22 @@ impl FractalRenderer {
         });
 
         Self {
-            pipeline,
+            iterate_pipeline,
+            export_pipeline,
             bind_group_layout,
             uniform_buffer,
             ref_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,
-            rendered: None,
+            iterated: None,
+            colored: None,
         }
     }
 
@@ -326,13 +434,29 @@ impl FractalRenderer {
             return;
         }
 
-        let texture = device.create_texture(&wgpu::TextureDescriptor {
-            label: Some("fractal cache"),
-            size: wgpu::Extent3d {
-                width,
-                height,
-                depth_or_array_layers: 1,
-            },
+        let extent = 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,
@@ -340,7 +464,22 @@ impl FractalRenderer {
             usage: wgpu::TextureUsages::RENDER_ATTACHMENT | wgpu::TextureUsages::TEXTURE_BINDING,
             view_formats: &[],
         });
-        let view = texture.create_view(&wgpu::TextureViewDescriptor::default());
+        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),
+                },
+            ],
+        });
 
         let blit_bind_group = device.create_bind_group(&wgpu::BindGroupDescriptor {
             label: Some("blit bind group"),
@@ -348,7 +487,7 @@ impl FractalRenderer {
             entries: &[
                 wgpu::BindGroupEntry {
                     binding: 0,
-                    resource: wgpu::BindingResource::TextureView(&view),
+                    resource: wgpu::BindingResource::TextureView(&color_view),
                 },
                 wgpu::BindGroupEntry {
                     binding: 1,
@@ -358,21 +497,30 @@ impl FractalRenderer {
         });
 
         self.cache = Some(CacheTarget {
-            view,
+            data_view,
+            color_view,
+            colorize_bind_group,
             blit_bind_group,
             width,
             height,
         });
-        // New texture → old render is gone.
-        self.rendered = None;
+        // New textures → old renders are gone.
+        self.iterated = None;
+        self.colored = 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.pipeline.clone(),
+            self.export_pipeline.clone(),
             self.bind_group_layout.clone(),
             self.target_format,
         )
@@ -412,7 +560,6 @@ impl ExportRender {
         height: u32,
         uniforms: Uniforms,
         reference: &[[f32; 2]],
-        bla: &[Bla],
     ) -> Self {
         let uniform_buffer = device.create_buffer(&wgpu::BufferDescriptor {
             label: Some("export uniforms"),
@@ -433,24 +580,20 @@ impl ExportRender {
             queue.write_buffer(&ref_buffer, 0, bytemuck::cast_slice(&reference[..count]));
         }
 
-        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,
+        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(),
+                },
+            ],
         });
-        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"),
@@ -634,13 +777,12 @@ 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
-/// 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.
+/// 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`).
 pub struct FractalCallback {
     pub uniforms: Uniforms,
     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],
@@ -670,28 +812,29 @@ 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;
         }
 
-        // Re-render the cache only when what it depends on changed.
-        let dirty = renderer.rendered.as_ref().is_none_or(|r| {
+        // 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| {
             r.generation != self.generation
                 || r.width != width
                 || r.height != height
-                || bytemuck::bytes_of(&r.uniforms) != bytemuck::bytes_of(&self.uniforms)
+                || geom_differs(&r.uniforms, &self.uniforms)
         });
-        if !dirty {
-            return Vec::new();
+        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)
+            });
+
+        if !color_dirty {
+            return Vec::new(); // cache still valid; paint() just blits it
         }
 
+        // Both passes read the uniform buffer; refresh it once.
         queue.write_buffer(
             &renderer.uniform_buffer,
             0,
@@ -699,10 +842,34 @@ impl egui_wgpu::CallbackTrait for FractalCallback {
         );
 
         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"),
+                    color_attachments: &[Some(wgpu::RenderPassColorAttachment {
+                        view: &cache.data_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.iterate_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 cache pass"),
+                label: Some("fractal colorize pass"),
                 color_attachments: &[Some(wgpu::RenderPassColorAttachment {
-                    view: &cache.view,
+                    view: &cache.color_view,
                     depth_slice: None,
                     resolve_target: None,
                     ops: wgpu::Operations {
@@ -715,14 +882,21 @@ impl egui_wgpu::CallbackTrait for FractalCallback {
                 occlusion_query_set: None,
                 multiview_mask: None,
             });
-            pass.set_pipeline(&renderer.pipeline);
-            pass.set_bind_group(0, &renderer.bind_group, &[]);
+            pass.set_pipeline(&renderer.colorize_pipeline);
+            pass.set_bind_group(0, &cache.colorize_bind_group, &[]);
             pass.draw(0..3, 0..1);
         }
 
-        renderer.rendered = Some(RenderedState {
+        if iter_dirty {
+            renderer.iterated = Some(IterState {
+                uniforms: self.uniforms,
+                generation: self.generation,
+                width,
+                height,
+            });
+        }
+        renderer.colored = Some(ColorState {
             uniforms: self.uniforms,
-            generation: self.generation,
             width,
             height,
         });

src/fractal/share.rs

@@ -21,6 +21,10 @@ 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).
@@ -31,18 +35,28 @@ 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 {
-            FractalKind::Mandelbrot => "mandel",
-            FractalKind::BurningShip => "burning",
-            FractalKind::Multibrot => "multi",
-            FractalKind::Tricorn => "tricorn",
-        }));
+        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
@@ -68,7 +82,12 @@ impl ShareState {
                     "multi" => FractalKind::Multibrot,
                     "burning" => FractalKind::BurningShip,
                     "tricorn" => FractalKind::Tricorn,
-                    _ => FractalKind::Mandelbrot
+                    "celtic" => FractalKind::Celtic,
+                    "perp" => FractalKind::Perpendicular,
+                    "buffalo" => FractalKind::Buffalo,
+                    "phoenix" => FractalKind::Phoenix,
+                    "lambda" => FractalKind::Lambda,
+                    _ => FractalKind::Mandelbrot,
                 })
                 .unwrap_or(FractalKind::Mandelbrot),
             power: map.get("pw").and_then(|s| s.parse().ok()).unwrap_or(2),
@@ -80,6 +99,14 @@ 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),
@@ -95,13 +122,15 @@ mod tests {
     fn round_trip() {
         let s = ShareState {
             julia: true,
-            kind: FractalKind::Multibrot,
+            kind: FractalKind::Phoenix,
             power: 5,
             center_re: "-0.743643887037158704752191506114774".into(),
             center_im: "0.131825904205311970493132056385139".into(),
             half_height: 1.5e-20,
             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,
@@ -115,6 +144,7 @@ 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);
     }
 

src/main.rs

@@ -1,3 +1,7 @@
+// 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
@@ -25,14 +29,13 @@ 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")]
         {
             setup.instance_descriptor.backends = wgpu::Backends::BROWSER_WEBGPU;

src/shaders/buddhabrot.wgsl

@@ -0,0 +1,299 @@
+// 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

@@ -0,0 +1,99 @@
+// 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,
+    aa_level: u32,
+    kind: u32,
+    power: u32,
+    dc_offset: vec2<f32>,
+    phoenix_p: vec2<f32>,
+    lambda_l: vec2<f32>,
+    de_coloring: u32,
+    shadow: u32,
+};
+
+@group(0) @binding(0) var<uniform> u: Uniforms;
+@group(0) @binding(1) var data_tex: texture_2d<f32>;
+
+// 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);
+}
+
+@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., 0.11, 0.54, 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]));
+
+            let color = (dot(normal, vec3<f32>(.5, .5, .5)) + 0.2) / 1.2;
+
+            return vec4<f32>(vec3<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

@@ -22,36 +22,35 @@ struct Uniforms {
     is_julia: u32,
     palette_id: u32,
     aa_level: u32,
-    // Iteration formula: 0 Mandelbrot, 1 Burning Ship, 2 Tricorn, 3 Multibrot.
+    // Iteration formula (see the KIND_* constants below).
     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 = 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,
+    // 0 = classic colors, 1 = shadows
+    shadow: 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 +88,7 @@ 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 +126,7 @@ 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
@@ -136,14 +135,35 @@ 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
+    return 2.0 * cmul(z, e) + cmul(e, e); // Mandelbrot (and Phoenix square part)
 }
 
 // Derivative f'(Z) of the iteration map at the full value Z, used to propagate
@@ -152,82 +172,55 @@ 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));
 }
 
-// Result of a BLA lookup at an orbit index.
-struct Hop {
-    found: bool,
-    a: vec2<f32>,
-    b: vec2<f32>,
-    l: u32,
+// 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,
 };
 
-// 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> {
+// 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 {
     let z0 = ref_orbit[0]; // reference start (0 for Mandelbrot, center for Julia)
 
     var step_add = offset;
@@ -236,7 +229,11 @@ fn shade(offset: vec2<f32>, px: f32) -> vec3<f32> {
     // (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);
-    if (u.is_julia != 0u) {
+    // 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 {
         step_add = vec2<f32>(0.0, 0.0);
         e = offset;
         dz = vec2<f32>(1.0, 0.0);
@@ -248,67 +245,66 @@ fn shade(offset: vec2<f32>, px: f32) -> vec3<f32> {
     var z = vec2<f32>(0.0, 0.0);  // full value y_n, kept for coloring
     var escaped = false;
 
-    loop {
-        let xm = ref_orbit[m];
-        z = xm + e;
+        loop {
+            let xm = ref_orbit[m];
+            z = xm + e;
 
-        let z2 = dot(z, z);
-        if (z2 > u.bailout_sq) {
-            escaped = true;
-            break;
-        }
-        if (n >= u.max_iter) {
-            break; // interior
-        }
+            let z2 = dot(z, z);
+            if z2 > u.bailout_sq {
+                escaped = true;
+                break;
+            }
+            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);
+        // 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;
                 }
-                e = cmul(hop.a, e) + cmul(hop.b, step_add);
-                m = m + hop.l;
-                n = n + hop.l;
-                did_skip = true;
+                dz = dz_new;
             }
-        }
-        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.
-            if (u.de_coloring != 0u) {
-                dz = cmul(fprime(z), dz) + dz_seed;
-            }
-            // Advance the delta by this fractal's formula (+ dc for the set plane).
+
+        // 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;
-            escaped = true;
-            break;
-        }
-        let y = ref_orbit[m] + e;
-        if (dot(y, y) < dot(e, e)) {
+                z = ref_orbit[u.ref_len - 1u] + e;
+                escaped = true;
+                break;
+            }
+            let y = ref_orbit[m] + 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.
-            e = y - z0;
-            m = 0u;
+            // 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 vec3<f32>(0.0, 0.0, 0.0); // interior of the set
+    if !escaped {
+        return Sample(0.0, 1.0, false); // interior of the set
     }
 
     let z2 = dot(z, z);
@@ -321,10 +317,9 @@ fn shade(offset: vec2<f32>, px: f32) -> vec3<f32> {
     // 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);
 
-    if (u.de_coloring != 0u) {
+    var de = 1.0;
+    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
@@ -332,37 +327,81 @@ fn shade(offset: vec2<f32>, px: f32) -> vec3<f32> {
         // 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 de = zmag * log(zmag) / dzmag;
-        let de_px = de / max(px, 1e-30);
-        col = col * clamp(de_px, 0.0, 1.0);
+        let d = zmag * log(zmag) / dzmag;
+        var max_de = 1.;
+        if u.shadow != 0u {
+            max_de = 1000.;
+        }
+        de = clamp(d / max(px, 1e-30), 0.0, max_de);
     }
-    return col;
+    return Sample(ci, de, true);
 }
 
-@fragment
-fn fs_main(in: VsOut) -> @location(0) vec4<f32> {
-    let base = in.centered * u.span + u.dc_offset;
+// 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;
+}
 
-    // 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.
+// 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> {
+    let base = in.centered * u.span + u.dc_offset;
     let dx = dpdx(base);
     let dy = dpdy(base);
-    let px = length(abs(dx) + abs(dy)); // ~ complex units per pixel (footprint)
+    let px = length(abs(dx) + abs(dy));
 
     let aa = max(u.aa_level, 1u);
-    if (aa <= 1u) {
-        return vec4<f32>(shade(base, px), 1.0);
-    }
-
-    var acc = vec3<f32>(0.0, 0.0, 0.0);
     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) {
-            // 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 + shade(base + jx * dx + jy * dy, px);
+            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);
+}
+
+// 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);
+    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;
+            acc = acc + color_sample(iterate_sample(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); // y-down -> imag-up
+        self.center_im = &self.center_im - &big_from_f64(dy * cpp, bits);
     }
 
     /// 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); // y flip
+        self.center_im = &self.center_im + &big_from_f64(off_y * k, bits);
         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::{Bla, FractalKind, build_bla_table, compute_reference, compute_set_reference};
+use crate::fractal::{FractalKind, 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,
-    /// 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,
+    /// 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),
 }
 
 pub struct RefResult {
@@ -33,7 +33,6 @@ pub struct RefResult {
     pub center_im: Big,
     pub half_height: f64,
     pub points: Vec<[f32; 2]>,
-    pub bla: Vec<Bla>,
 }
 
 pub struct RefWorker {
@@ -61,18 +60,12 @@ 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()
                     {
@@ -112,6 +105,8 @@ fn compute(req: &RefRequest) -> Vec<[f32; 2]> {
             req.precision,
             req.kind,
             req.power,
+            req.phoenix_p,
+            req.lambda_l,
         )
     } else {
         compute_set_reference(
@@ -121,6 +116,8 @@ fn compute(req: &RefRequest) -> Vec<[f32; 2]> {
             req.precision,
             req.kind,
             req.power,
+            req.phoenix_p,
+            req.lambda_l,
         )
     }
 }

tests/shader_valid.rs

@@ -25,7 +25,20 @@ 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"),
+    );
+}