#
Evolutionary Exploration of Generalized Julia Sets

Submitted to CIISP 2007

### Daniel Ashlock and Brooke Jamieson

Julia sets are fractal subsets of the complex plane defined by a
simple iterative algorithm. Julia sets are specified by a single
complex parameter and their appearances are indexed by the Mandelbrot
set. This study presents a simple generalization of the quadratic
Julia set that requires two complex parameters. The generalization
causes the Mandelbrot set indexing the generalized Julia sets to
become 4-dimensional and hence difficult to use as a visual index. An
evolutionary algorithm is used to search the space of generalized
quadratic Julia sets. A type of fitness function is presented that
permits the artist exert some control over the appearance of the
resulting Julia sets. The impact of different versions of the fitness
function on the resulting Julia sets is explored. It is found that
the designed fitness functions do give substantial control over the
appearance of the resulting fractals.