Chaotic attractors with symmetries of the triangle groups

The chaotic attractors with symmetries of the triangle groups are visualized in the hyperbolic plane. Using probabilistic iterated function systems that involve both affine transformations of the plane and isometries 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 with the triangle groups as well. The method provides a novel approach for devising tiling patterns with symmetries.