RecDiFF

Reaction and diffusion of chemical species can produce a variety of patterns, reminiscent of those often seen in nature. The Gray-Scott equations model such a reaction. What is special about such a model is that it can explain pattern formation without a preformed pattern. That is, the reaction-diffusion model can explain how those initial patterns form in the first place.

In the strict sense of the term, reaction-diffusion systems are systems involving constituents locally transformed into each other by chemical reactions and transported in space by diffusion. They arise, quite naturally, in chemistry and chemical engineering but also serve as a reference for the study of a wide range of phenomena encountered beyond the strict realm of chemical science such as environmental and life sciences.

Alan Turing

The evolution and development of animal form has been the subject of study for many evolutionary and developmental biologists. The prime model for animal development has been the fruit fly Drosophila melanogaster. While biologists now know flies are developmentally unique, fundamental models have been constructed to explain fly development. Several models have been theorized but no mathematical model has been as arguably influential as Alan Turing’s reaction-diffusion equations.

Alan Turing was not a biologist, but a mathematician and the founder of computer science. Well-known for cracking the Nazis’ Enigma Code during World War II, Turing sought to crack another kind of code – how animals could develop from chemical substrates. He believed development could be reduced to mathematical axioms and physical laws.

His landmark paper, “The Chemical Basis of Morphogenesis,” was published in 1952, two years before his enigmatic death. In it he theorized a system of two different interacting molecules, called morphogens, which could establish chemical gradients through a “reaction-diffusion system.”

The central idea behind the theory is that two homogeneously distributed substances within a certain space, one “locally activated” and the other capable of “long-range inhibition,” can produce novel shapes and gradients. The results of these substance interactions are dependent on just four variables per morphogen – the rate of production, the rate of degradation, the rate of diffusion and the strength of their activating/inhibiting interactions.

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Ed.  1. / 7 . AP

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The sculptures can be produced in different materials and sizes, e.g. copper, nickel, chrome, silver and gold (non-exhaustive list). Each material is de facto a limited edition.