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Patterns occur everywhere in nature: from snowflakes and leopards\' coat to the large-scale of the universe.

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Patterns occur everywhere in nature: from snowflakes and leopards' coat to the large-scale of the universe. One of the first scientists to present mathematical models describing the interaction between chemicals and its relation with morphogenesis was Alan Turing in his seminal paper entitled "The Chemical Basis of Morphogenesis" (Phil Trans Royal Soc London (B), 237(641):37-72, 1952; available here). Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way that they produce spatial patterns of chemical or morphogen concentrations. Mathematically, this is expressed by the following system of equations:

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