GPU accelerated fractal zoom.

src/slide/s6_fractals/compute.wgsl

+struct ComputeParams {
+    width: u32;
+    height: u32;
+    center_x: f32;
+    center_y: f32;
+    zoom: f32;
+};
+
+[[group(0), binding(0)]] var<uniform> params: ComputeParams;
+[[group(0), binding(1)]] var texture: [[stride(16)]] texture_storage_2d<rgba8unorm, write>;
+
+fn mandelbrot(x: f32, y: f32, cutoff: f32) -> f32 {
+    var x1: f32 = 0.0;
+    var y1: f32 = 0.0;
+    var i: f32 = 0.0;
+
+    loop {
+        if (x1 * x1 + y1 * y1 > 16.0 || i >= cutoff) {
+            break;
+        }
+
+        let x_tmp: f32 = x1 * x1 - y1 * y1 + x;
+        y1 = 2.0 * x1 * y1 + y;
+        x1 = x_tmp;
+        i = i + 1.0;
+    }
+
+    var fract = 1.0 - log(log(sqrt(max(1.001, x1 * x1 + y1 * y1)))) / log(2.0);
+    return (i + fract) / cutoff;
+}
+
+[[stage(compute), workgroup_size(8, 8)]]
+fn main([[builtin(global_invocation_id)]] global_id: vec3<u32>) {
+    let X: u32 = global_id.x;
+    let Y: u32 = global_id.y;
+    let W: u32 = params.width;
+    let H: u32 = params.height;
+
+    if (X >= W || Y >= H) {
+        return;
+    }
+
+    let aspect = f32(W) / f32(H);
+    let nx = f32(X) / f32(W) - 0.5;
+    let ny = f32(Y) / f32(H) - 0.5;
+    let fx = params.center_x + nx * params.zoom * aspect;
+    let fy = params.center_y + ny * params.zoom;
+
+    let max_iter = min(270.0, 32.0 + sqrt(16.0 / params.zoom));
+    let o = params.zoom * 0.2 / f32(W);
+    let iter = pow((mandelbrot(fx + o, fy + o, max_iter) + mandelbrot(fx + o, fy - o, max_iter) + mandelbrot(fx - o, fy + o, max_iter) + mandelbrot(fx - o, fy - o, max_iter)) * 0.25, 1.0);
+
+    // https://flatuicolors.com/palette/defo
+    var amethyst = vec3<f32>(155.0/255.0, 89.0/255.0, 182.0/255.0);
+    var wet_asphalt = vec3<f32>(52.0/255.0, 73.0/255.0, 94.0/255.0);
+    var emerald = vec3<f32>(46.0/255.0, 204.0/255.0, 113.0/255.0);
+    var sunflower = vec3<f32>(241.0/255.0, 196.0/255.0, 15.0/255.0);
+    var alizarin = vec3<f32>(231.0/255.0, 76.0/255.0, 60.0/255.0);
+    var pomegranate = vec3<f32>(192.0/255.0, 57.0/255.0, 43.0/255.0);
+    var peter_river = vec3<f32>(52.0/255.0, 152.0/255.0, 219.0/255.0);
+    var midnight_blue = vec3<f32>(44.0/255.0, 62.0/255.0, 80.0/255.0);
+
+    let count: i32 = 8;
+    var stops = array<vec3<f32>, 8>(
+        midnight_blue,
+        alizarin,
+        wet_asphalt,
+        amethyst,
+        peter_river,
+        pomegranate,
+        sunflower,
+        vec3<f32>(0.1, 0.1, 0.1)
+    );
+
+    let i = i32(iter * f32(count - 1));
+    let color = mix(stops[i], stops[i + 1], smoothStep(f32(i) / f32(count - 1), f32(i + 1) / f32(count - 1), iter));
+
+    textureStore(texture, vec2<i32>(i32(X), i32(Y)), vec4<f32>(color.x, color.y, color.z, 1.0));
+}
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