Chaotic attractors near forbidden symmetry

We explore chaotic attractors with symmetries that are close to forbidden symmetries. In particular, attractors with planar crystallographic symmetry that contain an imperfect, but apparent, rotation that does not preserve the lattice of translations are constructed. This gives us a visual representation of patterns which have low symmetry type, but which contain additional, provocative structure. Like Penrose tilings and diffraction patterns of quasicrystals, our constructions include local rotations that are forbidden from being global by classical crystallographic theory.