Chaotic attractors near forbidden symmetry

We explore chaotic attractors with symmetries that are dose to forbidden sy mmetries. In particular, attractors with planar crystallographic symmetry t hat contain an imperfect, but apparent, rotation that does not preserve the lattice of translations are constructed. This gives us a visual representa tion of patterns which have low symmetry type, but which contain additional , provocative structure. Like Penrose tilings and diffraction patterns of q uasicrystals, our constructions include local rotations that are forbidden from being global by classical crystallographic theory. (C) 2000 Elsevier S cience Ltd. All rights reserved.