Mandelbrot Set

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Who can forget the beautiful Mandelbrot set?  It is extraordinary simple yet infinitely complex.  Named after Benoit Mandelbrot, the formula behind it is as follows:

Z = Z ^ 2 + C

C must always remain bounded. 

The Mandelbrot set was discovered in 1980.  While this may seem surprising by how simple the formula is, it required supercomputers to accurately give a picture of the complexity of infinity.

 

Summum_Malum

Maybe you should also mention that $z\in \mathbb{C}$

pangalacticgogoblast

I never really get into the matter...but i think you should use some sort of recursive mechanism to get the autosimilarity stuff, in this case $z_{n}=z_{n-1}^{2}+cost$