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Turing Patterns. First edition of the rare true author's-presentation offprint of Turing's last major published work - the paper in which he showed how chemical diffusion through living tissue can break symmetry and organise itself into stable spatial pattern, founding the mathematical theory of biological pattern formation and standing now, of everything Turing wrote, as the most-cited. The present copy is the author's own presentation issue, and it carries an exceptional association: the ink ownership inscription of the plant morphologist Otto L. Stein, and, loosely inserted, a typed letter of 28 August 1956 from R. A. Brooker - Turing's successor at the Manchester Computing Machine Laboratory - answering the request for a reprint that Stein had posted, more than two years earlier, to Turing himself. Turing came to Manchester in 1948 as deputy director of the Royal Society Computing Machine Laboratory, and when the Ferranti Mark I was delivered there in February 1951 he had at last the machine on which to attack a question that had held him since he read D'Arcy Wentworth Thompson's On Growth and Form as a young man: how does biological matter, growing from a nearly uniform egg, decide where to put a limb, a stripe, a whorl of leaves? He told Mike Woodger at the National Physical Laboratory that one of the machine's first jobs would be 'to do something about "chemical embryology"' (Hodges, Alan Turing: The Enigma, p. 436), and worked at it through 1951, often at night. He told Robin Gandy the theory was meant 'to defeat the Argument from Design': where the biology of the day spoke vaguely of 'morphogenetic fields' endowing tissue with an invisible pattern, and where Michael Polanyi held that embryonic form admitted no mechanical explanation at all, Turing proposed to treat the field as nothing more than a distribution of chemical concentrations and to ask what such a distribution could do on its own. His answer is the paper's lasting contribution. Pattern, he showed, can arise from the interaction of diffusing, reacting chemical substances - he called them morphogens - by a mechanism that runs flatly against intuition. Diffusion alone smooths differences away and should erase any pattern; but Turing proved that in a system of two such substances reacting together, one diffusing faster than the other, the uniform state becomes unstable, so that the smallest random disturbance grows into a fixed, regular spatial pattern of concentration. He worked the case through on a ring of cells, classified the kinds of instability that can result, and computed a worked example by hand with the Ferranti's help - the 'dappled' figure on the paper's sixtieth page has since become the visual emblem of the whole field. The closing pages name the targets: the tentacles of Hydra, the whorl of leaves on a stem, the breaking of symmetry at gastrulation, the spots on an animal's coat, the Fibonacci spirals of a fir-cone. The mechanism - diffusion, the great smoother, made the engine of pattern - is what the world now calls the Turing instability, and its patterns Turing patterns. The paper appears in two forms, told apart by a single detail. The author's presentation offprint - the present copy - carries no price on its wrapper; the commercial reprint that Cambridge University Press sold to recover costs prints 'Price Eight Shillings' at the foot of the wrapper and of the first leaf. The Royal Society gave its authors about a hundred free offprints, so the presentation issue was always scarce, and surviving copies are rare in the trade. Institutional copies of the presentation issue are few: the Turing Archive at King's College Cambridge holds one, catalogued AMT/B/22, and a copy of the paper is reported in the Max Newman collection at Bletchley Park, though whether that copy is the presentation issue or the priced reprint is not documented. The benchmark at auction is the copy of Turing's wartime collaborator Donald Bayley, £12,800 at Bonhams in No.
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