Fractal Art based on "The Butterfly Effect" of Chaos Theory

Abstract

This paper proposes and demonstrates a new integration of the theory of fractals and the butterfly effect of chaos theory. They both have long histories in creating digital artworks, but besides of many existing fractal software programs, none of them allowed us to achieve the proposed integration. Moreover, our program is the first to provide the functional concepts of overlapping results and sequential transformations, which allow us to generate a wider variety of patterns. Our program not only has the potential of creating 2D digital artworks but also supports the creation of animated abstract artworks.