A two-dimensional numerical study of spatial pattern formation in interacting Turing systems

Abstract

For many years Turing systems have been proposed to account for spatial and spatiotemporal pattern formation in chemistry and biology. We extend the study of Turing systems to investigate the rôle of boundary conditions, domain shape, non-linearities, and coupling of such systems. We show that such modifications lead to a wide variety of patterns that bear a striking resemblance to pigmentation patterns in fish, particularly those involving stripes, spots and transitions between them. Using the Turing system as a metaphor for activator—inhibitor models we conclude that such a mechanism, with the aforementioned modifications, may play a rôle in fish patterning.