# Mandelbrot Set

1,010pages on
this wiki

The Mandelbrot Set is a set of complex numbers bounded by a fractal boundary.

The basic mandelbrot set is generated by the function:

$Z_0 = 0$
$Z_{n+1} = Z_n ^ 2 + C$
$C \in M \iff \limsup_{n \to \infty}|z_{n+1}| \leq 2.$

Where $C$ is a point on the Complex plane. While the mandelbrot set consists of points which do not diverge, the number of iterations required to escape the boundary is still of interest.