Computability and the Turing centenary

Fri, 2014-11-21 11:40 -- Helen Duriez

Editors: S. Barry Cooper and Philip Maini

Alan Turing inhabited a very individual world between the abstract and the concrete. In Manchester in the early 1950s, in one of the more remarkable switches of focus in scientific history, he turned his attention from man-made computing machines to the hidden mathematics of emergent form in nature. Turing's 1952 paper, ‘The chemical basis of morphogenesis’, was ground-breaking as it proposed for the first time that biological patterning arose as a self-organized emergent phenomenon in which, counterintuitively, instabilities leading to spatial pattern arise via the interaction of stablizing processes. The model, in its simplest form of a coupled system of reaction–diffusion equations, assumes that a chemical pre-pattern is set up to which cells respond by differentiating in a concentration-dependent manner. This paper has led to a rich literature in analyses (both mathematical and computational) of the model and variants thereof—together with biological/chemical experiments aiming to lend support to the model by identifying the chemicals (termed morphogens by Turing) that may be involved. This issue of Interface Focus illustrates how the model has been applied in biology and how, as experimental techniques have become more sophisticated increasing biological data, the models have been updated through identification of possible morphogens, and extensions of the basic model to include other mechanisms.

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This issue is published concurrently with a Phil. Trans. A issue The foundations of computation, physics and mentality: the Turing legacy organised by S Barry Cooper and Samson Abramsky.

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