Periodic pattern formation in reaction—diffusion systems: An introduction for numerical simulation

  • Takashi MiuraEmail author
  • Philip K. Maini
Review Article


The aim of the present review is to provide a comprehensive explanation of Turing reaction-diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction-diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for selforganization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction-diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology.

Key words

mathematical modeling numerical simulation pattern formation Turing 


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Copyright information

© Japanese Association of Anatomists 2004

Authors and Affiliations

  1. 1.Department of Human Anatomy and GeneticsKyoto University Graduate School of MedicineYoshida Konoe-Chou, Sakyo-kuJapan
  2. 2.Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordUK

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