Mandelbrot Example

A full Zust GPU numeric example

The Mandelbrot set shows Zust generics, BigFloat arithmetic, GPU kernel shape, typed vector output, and the SPIR-V, Metal, and Vulkan backend path.

Params Kernel Iteration Run

BigFloat Mandelbrot detail — BigFloat keeps deep coordinates stable so pixel offsets can still reveal boundary detail.

Mandelbrot spiral field — Higher iteration counts expose slow-escaping points, spirals, and fine structure.

Parameter struct

pub struct Params<N> {
    x: bigfloat::BigFloat<N>,
    y: bigfloat::BigFloat<N>,
    step: bigfloat::BigFloat<N>,
    max_iter: u32,
}

Mapping pixels to the complex plane

The GPU thread locates a sample, converts its pixel offset into BigFloat, and adds that offset to the high-precision center coordinate.

let px = group[0] * 16u32 + local[0];
let py = group[1] * 16u32 + local[1];

let x_bf = params.x.add(x_offset.mul(params.step));
let y_bf = params.y.add(y_offset.mul(params.step));

Escape iteration

The recurrence is `z = z² + c`. When `zx² + zy² > 4`, the point escapes; the escape count becomes the basis for smooth coloring.

Why BigFloat matters

In deep zooms, the complex-plane distance between neighboring pixels can be smaller than ordinary `f32` can preserve. BigFloat keeps the offsets meaningful.

Run it

cargo run -p vm-spirv --example mandelbrot

MANDEL_ZS=zusts/gpu/mandelbrot_bigfloat8.zs \
MANDEL_MODULE=mandelbrot_bigfloat8 \
cargo run -p vulkan --example run_mandel