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Interactive video lesson plan for: Can Math Explain How Animals Get Their Patterns?

Activity overview:

How Alan Turing's Reaction-Diffusion Model Simulates Patterns in Nature
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Reaction Diffusion Simulation (Gray-Scott model)


Credits (and Twitter handles):
Script Writer: Rachel Becker (@RA_Becks)
Script Editor: Emily Elert (@eelert)
Video Illustrator: Ever Salazar (@eversalazar)
Video Director: Emily Elert (@eelert)
Video Narrator: Emily Elert (@eelert)
With Contributions From: Henry Reich, Alex Reich, Kate Yoshida, Omkar Bhagat, Peter Reich, David Goldenberg
Music by: Nathaniel Schroeder:

Also, special thanks to the following scientists:
Greg Barsh: Investigator, HudsonAlpha Institute for Biotechnology (
Jeremy Green: Professor of developmental biology, King’s College London (
Thomas Hiscock: Graduate student in systems biology, Harvard University (
Shigeru Kondo: Professor, Osaka University (
James Sharpe: Coordinator of EMBL-CRG Systems Biology Unit and ICREA research professor (
Ian Stewart: Emeritus professor of mathematics, University of Warwick and author of The Mathematics of Life (
Thomas Woolley: Postdoctoral scientist, St John's College Oxford (

Image Credits:
- Mouse palate images provided courtesy of Jeremy Green, King’s College London.
- Digit patterns image provided courtesy of Luciano Marcon and Jelena Raspopovic.
- Angelfish and zebrafish images provided courtesy of Shigeru Kondo.

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Here are some handy keywords to get your googling started:

Reaction-diffusion system: A hypothetical system in which multiple chemical substances diffuse through a defined space at different rates and react with one another, thereby generating a pattern.

Turing pattern: A periodic pattern that forms in a space where the initial distribution of ‘activator’ and ‘inhibitor’ is the same.

Morphogenesis: The processes during development that give rise to the form or shape of the organism or a structure

Alan Turing: Alan Turing was a British mathematician and the father of modern computer science. During World War II, he broke Germany’s Enigma code used to encrypt communications.



Economou, A. D., Ohazama, A., Porntaveetus, T., Sharpe, P. T., Kondo, S., Basson, M. A., … Green, J. B. A. (2012). Periodic stripe formation by a Turing-mechanism operating at growth zones in the mammalian palate. Nature Genetics, 44(3), 348–351.

Economou, A. D., & Green, J. B. (2014). Modelling from the experimental developmental biologists viewpoint. Seminars in Cell & Developmental Biology, 35, 58-65. doi:10.1016/j.semcdb.2014.07.006

Green, J. B., & Sharpe, J. (2015). Positional information and reaction-diffusion: Two big ideas in developmental biology combine.Development, 142(7), 1203-1211. doi:10.1242/dev.114991

Kimura, Y. T. (2016, May 24). The mathematics of patterns. Retrieved from

Kimura, Y. T. (2014). The Mathematics of Patterns: The modeling and analysis of reaction-diffusion equations (Thesis, Princeton University). Http://

Kondo, S., & Asai, R. (1995). A reaction-diffusion wave on the skin of the marine angelfish Pomacanthus. Nature, 376(6543), 765-768. doi:10.1038/376765a0

Kondo, S., & Miura, T. (2010). Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation. Science, 329(5999), 1616-1620. doi:10.1126/science.1179047

Marcon, L., & Sharpe, J. (2012). Turing patterns in development: What about the horse part? Current Opinion in Genetics & Development, 22(6), 578-584. doi:10.1016/j.gde.2012.11.013

Raspopovic, J., Marcon, L., Russo, L., & Sharpe, J. (2014). Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients. Science, 345(6196), 566-570. doi:10.1126/science.1252960

Stewart, I. (2012). The mathematics of life. Philadelphia, PA: Basic Books. (

Turing, A. M. (1952). The Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237(641), 37-72. Retrieved from

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