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1952 article written by English mathematician Alan Turing
Turing's paper explained how natural patterns, such as stripes, spots, and spirals, like those of the
giant pufferfish , may arise.
"The Chemical Basis of Morphogenesis " is an article that the English mathematician
Alan Turing wrote in 1952.
[1] It describes how
patterns in nature , such as stripes and spirals, can arise naturally from a homogeneous, uniform state. The theory, which can be called a
reaction–diffusion theory of
morphogenesis , has become a basic model in
theoretical biology .
[2] Such patterns have come to be known as
Turing patterns . For example, it has been postulated that the protein
VEGFC can form Turing patterns to govern
the formation of lymphatic vessels in the
zebrafish embryo.
[3]
Reaction–diffusion systems
Reaction–diffusion systems have attracted much interest as a prototype model for
pattern formation . Patterns such as fronts, spirals, targets, hexagons, stripes and
dissipative solitons are found in various types of reaction-diffusion systems in spite of large discrepancies e.g. in the local reaction terms. Such patterns have been dubbed "
Turing patterns ".
[4]
Reaction–diffusion processes form one class of explanation for the
embryonic development of animal coats and skin pigmentation.
[5]
[6] Another reason for the interest in reaction-diffusion systems is that although they represent
nonlinear
partial differential equations , there are often possibilities for an analytical treatment.
[7]
[8]
[9]
See also
References
^
Turing, Alan (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 .
S2CID
120437796 .
^ Harrison, L.G. (1993). Kinetic Theory of Living Pattern .
Cambridge University Press .
^ Wertheim, Kenneth (2019).
"Can VEGFC form turing patterns in the Zebrafish embryo?" . Bulletin of Mathematical Biology . 81 (4): 1201–1237.
doi :
10.1007/s11538-018-00560-2 .
PMC
6397306 .
PMID
30607882 .
^ Wooley, 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 .
^ Meinhardt, H. (1982). Models of Biological Pattern Formation .
Academic Press .
^ Murray, James D. (9 March 2013).
Mathematical Biology . Springer Science & Business Media. pp. 436–450.
ISBN
978-3-662-08539-4 .
^ Grindrod, P. Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations, Clarendon Press (1991)
^ Smoller, J. Shock Waves and Reaction Diffusion Equations, Springer (1994)
^ Kerner, B. S. and Osipov, V. V. Autosolitons. A New Approach to Problems of Self-Organization and Turbulence,
Kluwer Academic Publishers (1994).