Evolving fractal art with a directed acyclic graph genetic programming representation

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.