Fourier analysis of Turing-like pattern formation in cellular automaton models

被引：21

作者：

Dormann, S ^{[1
]}

Deutsch, A

Lawniczak, AT

机构：

[1] Univ Osnabruck, Dept Math, D-49069 Osnabruck, Germany

[2] Max Planck Inst Phys Complex Syst, D-01187 Dresden, Germany

[3] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada

[4] Fields Inst Res Math Sci, Toronto, ON M5T 3J1, Canada

来源：

FUTURE GENERATION COMPUTER SYSTEMS | 2001年 / 17卷 / 07期

关键词：

cellular automaton; lattice-gas automaton; Turing pattern; mean-field analysis; Boltzmann equation;

D O I：

10.1016/S0167-739X(00)00068-6

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The novelty of this paper is the study of emergence of diffusion-induced (Turing-like) patterns from a microscopic point of view, namely, in terms of cellular automata. Formally, the cellular automaton model is described in lattice-gas terminology [H. Bussemaker, A. Deutsch, E. Geigant, Phys. Rev. Lett. 78 (1997) 5018-5021]. The automaton rules capture in abstract form the essential ideas of activator-inhibitor interactions of biological systems. In spite of the automaton's simplicity, self-organised formation of stationary spatial patterns emerging from a randomly perturbed uniform state is observed. Fourier analysis of approximate mean-field kinetic difference equations [J.P. Boon, D. Dab, R. Kapral, A.T. Lawniczak, Phys. Rep. 273 (1996) 55-147] yields a critical wave length and a "Turing condition" for the onset of pattern formation. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：901 / 909

页数：9

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