Forma, Vol. 18 (No. 1), pp. 3-18, 2003

Pattern Selection and the Direction of Stripes in Two-Dimensional Turing Systems for Skin Pattern Formation of Fishes

Hiroto Shoji* and Yoh Iwasa

Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan
*E-mail address:

(Received November 29, 2002; Accepted December 25, 2002)

Keywords: Reaction-Diffusion System, Turing, Pattern Selection, Anistropic Diffusion, Directionality of Stripes

Abstract. Turing mechanism explains the pattern formation 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 spatial patterns either with stripes or with spots, and have been adopted to explain the skin pattern formation of animals. We first discuss the effect of the choice of reaction terms on pattern selection, whether spots or stripes are formed. It is shown that the relative distance of the equilibrium level of activator between the upper and lower limitations has a very strong effect on the pattern selection. Secondly, we 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 horizontal.

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