Abstract

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, ‘The chemical basis of morphogenesis’, on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of ‘Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Highlights

  • Let me begin my exploration of Alan Turing’s paper [1] in what might seem an unlikely and unpromising place: the list of references

  • Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, ‘The chemical basis of morphogenesis’, on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology

  • While no one could reasonably assert that this paper has had as profound an impact on biology as that published a year later by Watson and Crick on the structure of DNA, it surpasses their achievement in this one regard: before Turing, no one had even really thought to ask the question that he poses

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Summary

Introduction

Let me begin my exploration of Alan Turing’s paper [1] in what might seem an unlikely and unpromising place: the list of references. That was the central question that Turing addressed He presents a theoretical model in which chemicals that are diffusing and reacting may produce neither bland uniformity nor disorderly chaos but something in between: a pattern. This notion is, as we shall see, not entirely without precedent, but no one previously had thought to relate such an abstruse phenomenon to the question of biological growth and form— in short, to suggest how chemistry alone might initiate the process that leads from a ball of cells to a starfish, a horse or to us

The codebreaker
On growth and form
Chemical waves
But are they real?
Blossoming theory
Conclusion
53. New York

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