Mathematical Models for Pattern Formation of Fish Skin
Turing mechanism explains the pattern in a uniform field in which two substances (e.g. activator and inhibitor ) interact locally and diffuse randomly. Two-dimensional Turing models can generate stationary striped patterns or spotted patterns, and used to explain the body pattern formation of animals. I first discuss the effect of the choice of reaction terms on pattern selection, i.e., which pattern is likely to be formed. It is shown that the relative distance of the equilibrium level of activator between the upper and lower limitation has a very strong effect on the pattern selection. Secondly, I focus on the direction of the stripes generated by Turing model with anisotropic diffusion in order to explain the directionality of stripes on fish skin in closely related species. Relative magnitude of anisotropy of the two substances is shown to determine whether stripes are vertical or holizontal.