Turing pattern

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Three examples of Turing patterns
Six states generating a Turing pattern
A Turing bifurcation pattern
An example of a natural Turing pattern on a giant pufferfish

The concept of a Turing pattern (often referred to in the plural as Turing patterns) was introduced by the English mathematician Alan Turing in a 1952 paper entitled The Chemical Basis of Morphogenesis.[1] This foundational paper describes the way in which patterns in nature such as stripes and spots can arise naturally out of a homogeneous, uniform state.


The original theory, a reaction–diffusion theory of morphogenesis, has served as an important model in theoretical biology.[2] Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. Patterns such as fronts, hexagons, spirals, stripes and dissipative solitons are found in various types of reaction-diffusion systems, despite large discrepancies, in the local reaction terms for example. It is a major theory in developmental biology; for example, there was a theoretical study on the potential of VEGFC to form Turing patterns to regulate lymphangiogenesis in the zebrafish embryo[3].

As well as in biological organisms, Turing patterns occur in other natural systems – for example, the wind patterns formed in sand. Although Turing's ideas on morphogenesis and Turing patterns remained dormant for many years, they are now inspirational for much research in mathematical biology.[4]

See also[edit]


  1. ^ Turing, A. M. (1952). "The Chemical Basis of Morphogenesis" (PDF). Philosophical Transactions of the Royal Society of London B. 237 (641): 37–72. Bibcode:1952RSPTB.237...37T. doi:10.1098/rstb.1952.0012. JSTOR 92463.
  2. ^ Harrison, L. G. (1993). Kinetic Theory of Living Pattern. Cambridge University Press.
  3. ^ Roose, Tiina; Wertheim, Kenneth Y. (2019-01-03). "Can VEGFC Form Turing Patterns in the Zebrafish Embryo?". Bulletin of Mathematical Biology: 1–37. doi:10.1007/s11538-018-00560-2. ISSN 1522-9602. PMID 30607882.
  4. ^ Woolley, T. E., Baker, R. E. Maini, P. K., Chapter 34, Turing's theory of morphogenesis. In Copeland, B. Jack; Bowen, Jonathan P.; Wilson, Robin; Sprevak, Mark (2017). The Turing Guide. Oxford University Press. ISBN 978-0198747826.