Before revision:  We find spatial patterns of oscillating quasi-cycles that resemble Turing patterns , called quasi-patterns.
After revision:  Quasi-cycles are a proposed mechanism for the production of neural oscillations, and Mexican Hat coupling is ubiquitous in the brain. Thus this combination might provide insight into the function of neural oscillations in the brain. Importantly, we study this system only in the transient case, on time intervals before saturation occurs. In one dimension, for weak coupling, we find that the phases of the coupled quasi-cycles synchronize (establish a relatively constant relationship, or phase lock) rapidly at coupling strengths lower than those required to produce spatial patterns of oscillating quasi-cycles that resemble Turing patterns , called quasi-patterns.