Black-eye patterns: a representation of three-dimensional symmetries in thin domains.

ABSTRACT

What is believed to be the first experimental evidence for Turing patterns was observed in the CIMA reaction by De Kepper and colleagues. Ouyang and Swinney performed further experiments in a "thin" layer of gel. Patterns observed at onset were basically two-dimensional. However, beyond onset a structure that does not typically occur in two-dimensional domains was observed-the black-eye pattern. In this paper we use the full three-dimensionality of the patterned layer to find a setting where black-eye patterns naturally occur. We propose that black-eye patterns have the symmetry of a body-centered-cubic lattice.