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Mandelbrot Set

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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.

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