Automatic Generation of Chaotic Attractors with Various Cyclic or Dihedral Symmetries

Abstract

Chaotic attractors are created by iterating functions that are equivariant with respect to the cyclic or dihedral groups. An improved color scheme based on the visit frequency of the pixels is proposed to render chaotic attractors. By normalization and scale transformation, aesthetic patterns which simultaneously have several kinds of cyclic or dihedral symmetries are generated. This method can be used to yield a great number of aesthetic patterns automatically.