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.