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Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’

Krause, Andrew L. and Gaffney, Eamonn A and Maini, Philip K. and Klika, Václav (2021) 'Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.', Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379 (2213).


Elucidating pattern forming processes is an important problem in the physical, chemical and biological sciences. Turing’s contribution, after being initially neglected, eventually catalysed a huge amount of work from mathematicians, physicists, chemists and biologists aimed towards understanding how steady spatial patterns can emerge from homogeneous chemical mixtures due to the reaction and diffusion of different chemical species. While this theory has been developed mathematically and investigated experimentally for over half a century, many questions still remain unresolved. This theme issue places Turing’s theory of pattern formation in a modern context, discussing the current frontiers in foundational aspects of pattern formation in reactiondiffusion and related systems. It highlights ongoing work in chemical, synthetic and developmental settings which is helping to elucidate how important Turing’s mechanism is for real morphogenesis, while highlighting gaps that remain in matching theory to reality. The theme issue also surveys a variety of recent.

Item Type:Article
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Publisher statement:Creative Commons Attribution License by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Date accepted:23 August 2021
Date deposited:21 February 2022
Date of first online publication:08 November 2021
Date first made open access:21 February 2022

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