Reaction–Diffusion Equations and Cellular Automata

  • Mikio MurataEmail author
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 28)


A systematic approach to the construction of cellular automata that are analogs for the reaction–diffusion equations is presented. By using this method for the Allen–Cahn equation and the Gray–Scott model, cellular automatons are constructed. The solutions of the cellular automatons obtained by this method are similar to the solutions of the original reaction–diffusion equations.


Reaction–diffusion equation Cellular automaton Discretization Ultradiscretization 



This work was supported by JSPS KAKENHI Grant Number 16K21024.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Institute of EngineeringTokyo University of Agriculture and TechnologyKoganei-shi, TokyoJapan

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