Chaotic attractors with symmetries of the triangle groups

Abstract

The chaotic attractors with symmetries of the triangle p u p s are visualized in the hyperbolic plane. Using probabilistic iterated function systems that involve both &ne transformations of the plane and isometrjes of triangle groups, we can create intriguing and exotic attractor's images. The derived images are of self-similarity and of infinitely fine structure; they contain symmetries associated w i t h the triangle groups as well. The method provides a novel approach fur devising tiling patterns with symmetries.