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Forging patterns and making waves from biology to geology: a commentary on Turing
(1952) The chemical basis of morphogenesis
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Philos Trans R Soc Lond B Biol Sci
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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.