Chaotic attractors with cyclic symmetry revisited

Abstract

Chaotic attractors generated by the iteration of polynomial functions with cyclic symmetry have been the subject of recent study. A new formulation is investigated which generates cyclic symmetry using arbitrary functions. This allows the use of diverse function classes including functions with various types of singularities. The resulting images have significantly more diversity than those arising from polynomials, yet the cyclic symmetry of the chaotic attractor is preserved.