In “Symmetry in Chaos, A Search for Pattern in Mathematics, Art, and Nature,” Field and Golubitsky explore the possibility of aperiodic chaotic attractors generating symmetric patterns. They present a formula and parameters for the attractors, with the degree of symmetry determined by an integer n. The images shown are generated by iterating the series multiple times and then treating the complex plane as a 2D histogram. The histogram values are mapped onto colors to create the final image. The authors provide a rough guide to the parameters and note that finding “interesting” results is difficult due to the large parameter space.
http://paulbourke.net/fractals/symmetryinchaos/