TESSELLATIONS WITH SYMMETRIES OF THE TRIANGLE GROUPS FROM DYNAMICS

Abstract

A new and fast algorithm is presented in this paper for the automatic generation of aesthetic patterns with symmetries of the triangle groups T(p, q, r) by means of dynamical systems. Equivariant mappings with such symmetries are constructed. A modified convergence time scheme is described, which reflects the rate of convergence of various orbits and, at the same time, enhances the artistic appeal of generated images. Symmetrical chaotic attractors are generated by using a random iteration scheme. This method can be used to create a great variety of exotic symmetrical patterns.