What is Chemical Potential?

Exploring the patterns created by reaction-diffusion equations - rns.

The concept of a Turing pattern (often referred to in the plural as Turing patterns) was introduced by the English mathematician Alan Turing in a 1952 paper entitled The Chemical Basis of Morphogenesis. This foundational paper describes the way in which patterns in nature such as stripes and spots can arise naturally out of a homogeneous, uniform state. The original theory, a reaction–diffusion theory of morphogenesis, has served as an important model in theoretical biology.

Three examples of Turing patterns. A Turing bifurcation pattern. As well as in biological organisms, Turing patterns occur in other natural systems – for example, the wind patterns formed in sand, Turing patterns can also be created in nonlinear optics as demonstrated by the Lugiato–Lefever equation. Evolutionary developmental biology.

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His paper Cyclic Symmetric Mutli-Scale Turing Patterns explains a process that creates very interesting looking images like the following. Set all the values to the same starting color.

Alan Turing (1912-1954). Turing Patterns in Animal Coats. Junping Shi. Alan Turing (1912-1954). One of greatest scientists in 20 th century Designer of Turing machine (a theoretical computer) in 1930’s Breaking of U-boat Enigma, saving battle of the Atlantic Initiate nonlinear theory of biological growth.

Alan Turing (June 23, 1912–June 7, 1954) is celebrated as the godfather of modern computing, but what remains practically unknown is his seminal contribution to an obscure branch of biology: Turing dedicated a significant portion of his life to the study of morphogenesis - the biological process by which organisms take their shape. Among the materials, donated in 1960 by Turing’s mother and later digitized by . Furbank at the Archive, is a set of Turing’s hand-drawn, hand-colored morphogenesis diagrams - eerily beautiful visual explorations of dappling patterns, leaf arrangements, and daisy rings, somehow reminiscent of Kandinsky and mid-century graphic design.

Translation into German by Rolf Herken and Eva Lack: Alan Turing, Enigma, ISBN 3-211-82627-0, Springer Verlag, Wien. Translation into Italian by David Mezzacapa: Storia di un Enigma, ISBN 88-339-0639-6, Bollati Boringhieri.