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A lan Turing’s crucial intelligence work in the Second World War is well known. His contribution to the interdisciplinary field of mathematics and the biological sciences is less so. Turing published only one paper related to biology, “The chemical basis of morphogenesis”, in 1952 [64], which has been seminal in several areas of spatial patterning modeling in development, ecology, and other biological areas since its rediscovery in the 1960s. He did not apply his model to any specific biological situation. Basically Turing showed how, in a system of reacting chemicals where the chemicals can also diffuse, the system can generate a steady-state heterogeneous spatial pattern of chemical concentrations. He called these chemicals morphogens. Hehypothesizedthat thesemorphogeneticprepatterns could cue cell differentiation and result in observed spatial patterns. His model is encapsulated in the coupled system of reaction diffusion equations, of the general form (1) ∂u

Why Are There No 3-Headed Monsters? Mathematical Modeling in Biology