Mathematical Background

The Mandelbrot set is defined by the iteration:
zn+1 = zn² + c

Where z0 = 0 and c is a complex number corresponding to each pixel. Points remain bounded (in the set) if |zn| ≤ 2 for all iterations.

Julia sets use the same iteration but with fixed c and varying z0.

Colors represent escape velocity - how quickly points diverge to infinity.