Related Experiment Video
Updated: Aug 21, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Periodic pattern formation in reaction-diffusion systems: an introduction for numerical simulation
Takashi Miura1, Philip K Maini
1Department of Human Anatomy and Genetics University of Oxford, UK. miura-takashi@umin.ac.jp
Abstract:
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 self-organization 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.
Related Concept Videos
Reaction Mechanisms: The Steady-State Approximation
Fast Reactions
Consecutive Reactions
Reaction Mechanisms: Rate-limiting Step Approximation
Temperature Dependence on Reaction Rate
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...
Multi-Step Reactions

