Evolutionary computation to search Mandelbrot sets for aesthetic images
Daniel Ashlock, Brooke Jamieson · Journal of Mathematics and the Arts · 2007
We describe an evolutionary algorithm for searching Mandelbrot sets for aesthetic images. Artistic intent is enforced through the design of fitness functions that drive the evolutionary search. Our fitness function employs a mask that specifies a desired iterative behaviour at sample points within the image. The mask used to define a specific instance of the fitness function can be derived from an existing image of the Mandelbrot set. Because of this the artist need not be skilled in programming or familiar with the arithmetic of complex numbers. Once a mask has been chosen, our method uses an evolutionary algorithm to perform a three-parameter search of a specified Mandelbrot set. This paper applies our techniques to the quadratic and cubic Mandelbrot sets.