Building an Interactive Fractal Explorer

Three Challenges

The Lab generates Mandelbrot and Julia images with adjustable parameters and viewports. Interactive fractal explorers raise three useful engineering questions: performance, numerical precision, and progressive detail. The techniques below describe ways to address them; the current Lab uses CPU raster generation.

GPU-Accelerated Rendering

An escape-time iteration can run in a WebGL fragment shader. Each pixel computes its own iteration count independently, making the Mandelbrot set well suited to parallel GPU execution. Actual rendering time depends on the device, image dimensions, iteration limit and chosen region.

// Fragment shader (GLSL) — core iteration
vec2 z = vec2(0.0);
for (int i = 0; i < MAX_ITER; i++) {
  if (dot(z, z) > 4.0) { iter = i; break; }
  z = vec2(
    z.x*z.x - z.y*z.y + c.x,
    2.0*z.x*z.y + c.y
  );
}

Deep Zoom Precision

Precision becomes an issue at deep zoom levels when adjacent pixel coordinates become too close for the chosen numeric representation. Perturbation methods address this by computing a high-precision reference orbit on the CPU and expressing nearby pixels as small differences from that reference. This is an advanced rendering technique, not a feature of the current Lab generator.

Progressive Rendering

Progressive rendering can start with a coarse grid and refine it in later passes. This gives a viewer an early approximation while expensive detail is still being computed. Color mappings can then translate iteration values into a palette. These are design options for a fractal explorer; the current Lab renders its raster result as a completed image.