The Mandelbrot set is a mathematical marvel that reveals intricate, self-replicating patterns at every scale. This page explores how we're using modern computational methods to render it in new ways.
- Infinite complexity through simple math
- Zoom levels beyond traditional renderers
Mathematical Foundations
The Mandelbrot set is defined as the set of complex numbers c for which the function f_c(z) = z² + c does not diverge when iterated from z = 0.
z_{n+1} = z_n^2 + c
This deceptively simple formula produces infinite complexity through recursive iterations.
Modern Rendering
We use WebGL and Compute Shaders to render millions of iterations in real-time at 60+ FPS, with GPU-powered precision for infinite zooming and panning.
Interactive visualization of the set's fractal patterns with dynamic color palettes.
Computational Methods
// WebGL Shader Fragment
precision highp float;
uniform sampler2D u_iterations;
void main() {
vec2 uv = (gl_FragCoord.xy/u_resolution.xy) * 2.0 - 1.0;
float iterations = texture2D(u_iterations, uv).r;
gl_FragColor = vec4(hslToRgb(vec3( (iterations/1000.0), 0.8, 0.5)), 1.0);
}
We leverage GLSL shaders to calculate iterations in parallel. This enables performance at resolutions up to 8K with dynamic rendering.
- Adaptive max iterations based on zoom level
- GPU-accelerated color mapping algorithms
- Real-time zoom with hardware interpolation
Dive Deeper into the Mandelbrot
Join our community to share discoveries and explore new visualization techniques in fractal rendering.