1 Evolving the Mandelbrot Set to Imitate Figurative Art

Abstract. This chapter describes a technique for generating semi-abstract figurative imagery using variations on the Mandelbrot Set, evolved using a genetic algorithm. The Mandelbrot Set offers an infinite supply of complex fractal imagery, but its expressive ability is limited, as far as being a “material ” for visual manipulation by artists. The technique described here achieves a unique and varied brand of imagery by manipulating the mathematical function that generates the Set in a way that might seem unsavory from the standpoint of complex analysis – but it is very rich in terms of visual possibilities. Inspired by the author’s earlier interest in creating animalistic and pseudo-figurative forms by tweaking the function, a technique was developed to evolve figurative forms using a digital image as the objective fitness function for a genetic algorithm. Experiments reveal that the function has limits in terms of its ability to generate forms that imitate specific detailed images. But this is actually a desired quality, as it lends an enigmatic quality to the resulting artworks. These limitations also elicit questions about the ability for parametrically-based imaging systems (like fractals) to produce representational art. The analogy to genetics and animal morphology is presented, and this is used as a framework to describe the behavior of the Set as it is tweaked, and pulled “out of the complex plane ” (the canvas upon which the Set is normally painted). It provides a genetic vocabulary for describing, and thinking about, figurative art-making.