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You are here: Home / Associated publications / Belgian Journal of Zoology / Bibliographic References / Fifty years after Alan M. Turing - An extraordinary theory of morphogenesis

W Allaerts (2003)

Fifty years after Alan M. Turing - An extraordinary theory of morphogenesis

BELGIAN JOURNAL OF ZOOLOGY, 133(1):3-14.

The publication of `The Chemical Basis of Morphogenesis' by ALAN M. TURING in 1952 was a milestone for the development of mathematical biology and for many (biological) disciplines leaning on it. TURING provided an original solution to the problem of morphogenesis, by adapting a system of coupled differential equations to describe both chemical reaction and diffusion of morphogenetic substances in an initially homogeneous configuration. FOURIER'S analysis of the `ring problem' in heat conduction, and the theory of spherical harmonies and their solution by (normalized) LEGENDRE's associated functions form the mathematical backbone of TURING's work on morphogenesis. TURING was up to more than providing a mathematical description of initial stages of embryonic development. Rather he was eager to unveil the mathematical foundations of living, biological organization. An investigation of the archival material of unpublished letters and manuscripts indicates that TURING was clearly determined to provide an argument for the generation of `order-from-disorder'. Unfortunately, during his lifetime TURING remained unable to demonstrate the use of his model beyond the level of early embryonic stages. In the posthumously-published manuscripts several indications are found for further adaptation and improvement of TURING'S model to handle more accurately the reaction-diffusion processes in small organisms.

morphogenesis; reaction-diffusion theory; early embryonic development; spherical harmonics; normalized Legendre associated functions
BJZ

ISSN 2295-0451 (online version)
ISSN 0777-6279 (printed version)
impact factor 2015: 0,87.

Editor-in-Chief:
Prof. Dr. Isa Schön
Royal Belgian Institute of Natural Sciences
Vautierstraat 29
1000 Brussels, Belgium

 



1863-1903
Annales de la Société malacologique de Belgique
 
1903-1923
​Annales de la Société royale malacologique et zoologique de Belgique
 
1923-1989
Annales de la Société Royale Zoologique de Belgique
 
1989-
Belgian Journal of Zoology