Hardware Heritage
The Mandelbrot set is the ultimate test of mathematical precision and computational endurance. In the 80s and 90s, generating these infinite patterns was a rite of passage for every demoscene coder, serving as both a visual wonder and a benchmark for the machine's raw floating-point performance.
PC Benchmarking
On PC, fractals were the ultimate test of raw CPU power. Early adopters of the 80287 and 80387 co-processors would use Mandelbrot generators to prove their hardware was worth the high price tag.
Amiga FPU
Amiga users with specialized hardware (like the 68881/68882 FPUs) could generate fractals much faster than the base 68000. It was a common "hobbyist" task to see who could zoom deepest into the set.
Modern Precision
Modern hardware calculates hundreds of iterations per pixel in real-time. The only limit is 32-bit floating point precision, which eventually causes "pixelation" during extreme zooms.
Mandelbrot Set
Visualizing the boundary of infinite complexity.
Legacy C (Fixed Point)
for (iter=0; iter < MAX; iter++) {
// (x + iy)^2 = x^2 - y^2 + i(2xy)
long x2 = (zx * zx) >> 12;
long y2 = (zy * zy) >> 12;
if (x2 + y2 > (4 << 12)) break;
zy = ((zx * zy) >> 11) + cy;
zx = x2 - y2 + cx;
}
Modern GLSL
for(float i=0.0; i < 128.0; i++) {
z = vec2(z.x*z.x - z.y*z.y, 2.0*z.x*z.y) + c;
if(length(z) > 2.0) break;
iter++;
}