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Directed graph GP for evolving fractals

Submitted to CEC2015

### Daniel Ashlock and Jeffrey Tsang

A class of fractals called orbit capture fractals are generated by
iterating a function on a point until the point's trajectory enters a
capture zone. This study uses a digraph based representation for
genetic programming to evolve functions used to generate orbit capture
fractals. Three variations on the genetic programming system are
examined using two fitness functions. The first fitness function
maximizes the entropy of the distribution of capture numbers, while
the second places a geometric constraint on the distribution of
capture numbers. Some combinations of representation and fitness
function generate fractals often, while others yield interesting
non-fractal images most of the time.