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The Turing Model for Biological Pattern Formation

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The Dynamics of Biological Systems

Part of the book series: Mathematics of Planet Earth ((MPE,volume 4))

Abstract

How spatial patterning arises in biological systems is still an unresolved mystery. Here, we consider the first model for spatial pattern formation, proposed by Alan Turing, which showed that structure could emerge from processes that, in themselves, are non-patterning. He therefore went against the reductionist approach, arguing that biological function arises from the integration of processes, rather than being attributed to a single, unique, process. While still controversial, some 65 years on, his model still inspires mathematical and experimental advances.

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Acknowledgements

PKM and TEW would like to thank the Mathematical Biosciences Institute (MBI) at Ohio State University, for financially supporting this research through the National Science Foundation grant DMS 1440386. TEW would also like to acknowledge financial support from St John’s College, Oxford and BBSRC grant BKNXBKOO BK00.16.

The zebra skin, serval, arrow frog and x-ray pictures from Fig. 7.1 are used under creative commons license 2.0. They were downloaded from flickr.com and owned by David Richards, Vince Smith, The Reptilarium and Rahim Packir Saibo, respectively.

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Authors and Affiliations

  1. Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK

    Philip K. Maini

  2. School of Mathematics, Cardiff University, Cardiff, UK

    Thomas E. Woolley

Authors
  1. Philip K. Maini
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  2. Thomas E. Woolley
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Correspondence to Philip K. Maini .

Editor information

Editors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Arianna Bianchi

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Thomas Hillen

  3. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Mark A. Lewis

  4. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Yingfei Yi

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Maini, P.K., Woolley, T.E. (2019). The Turing Model for Biological Pattern Formation. In: Bianchi, A., Hillen, T., Lewis, M., Yi, Y. (eds) The Dynamics of Biological Systems. Mathematics of Planet Earth, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-22583-4_7

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