Construction of an Isotropic Cellular Automaton for a Reaction--Diffusion Equation by Means of a Random Walk

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概要

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• We propose a new method to construct an isotropic cellular automaton corresponding to a reaction--diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction--diffusion equation with random walk of microscopic particles and a discrete vector field which defines time evolution of the particles. The obtained cellular automaton can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction--diffusion equation. As a specific example, we apply the method to the Belousov--Zhabotinsky reaction in excitable media.

• Physical Society of Japanの論文
• 2011-05-15

著者

• Nishiyama Akinobu

  Graduate School Of Mathematical Science University Of Tokyo

• Tokihiro Tetsuji

  Graduate School Of Mathematical Science University Of Tokyo

• Nishiyama Akinobu

  Graduate School of Mathematical Sciences, The University of Tokyo, Meguro, Tokyo 153-8914, Japan

• Tokihiro Tetsuji

  Graduate School of Mathematical Sciences, The University of Tokyo, Meguro, Tokyo 153-8914, Japan

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