Fitness functions for searching the Mandelbrot set

The Mandelbrot set is a famous fractal. It serves as the source of a large number of complex mathematical images. Evolutionary computation can be used to search the Mandelbrot set for interesting views. This study compares the results of using several different fitness functions for this search. Some of the fitness functions give substantial control over the appearance of the resulting views while others simply locate parts of the Mandelbrot set in which there are complicated structures. All of the fitness functions are based on finding desirable patterns in the number of iterations of the basic Mandelbrot formula to diverge on a set of points arranged in a regular grid near the boundary of the set. It is shown that using different fitness functions causes an evolutionary algorithm to locate difference types of views into the Mandelbrot set.