The Turing Guide

362 | 33 PIONEER Of ARTIfICIAl lIfE Turing’s intoxicating paper clearly supplied that ‘smallest beginning’. And although it was ...

BODEN | 363 and (when dealing with multicellular structures) the number and spatial dimensions of the cells. He showed that cert ...

364 | 33 PIONEER Of ARTIfICIAl lIfE was that he couldn’t give a mathematical account of the origin of novel structure from some ...

BODEN | 365 Our simple, or simplified, illustrations carry us but a little way, and only half prepare us for much harder things  ...

366 | 33 PIONEER Of ARTIfICIAl lIfE didn’t say that he was already working on a computable theory of how chemicals can guide the ...

BODEN | 367 figure 33.4 Complex naturalistic patterns. Reproduced from G. Turk, ‘Generating textures on arbitrary surfaces using ...

368 | 33 PIONEER Of ARTIfICIAl lIfE The more recent Turing-inspired models of biological self-organization go far beyond Turk’s ...

BODEN | 369 each of the little tips (calcium peaks) would have to behave (to soften, bulge, and grow) like the main tip, but on ...

370 | 33 PIONEER Of ARTIfICIAl lIfE Now, half a century later, such machines exist—and they are invaluable in the study of spe- ...

BODEN | 371 Buried treasure In 1940, when England was expecting a Nazi invasion, Turing buried some silver bars in the grounds o ...

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CHAPTER 34 Turing’s theory of morphogenesis thomas e. woolley, ruth e. baker, and philip k. maini I n 1952, Turing proposed a ma ...

374 | 34 TURING’S THEORy Of mORPHOGENESIS Turing’s equations The theory is that patterns arise as the consequence of an observab ...

wOOllEy, BAkER, & mAINI | 375 To illustrate this idea, let us use a fictitious example involving ‘sweating grasshoppers’.^3 ...

376 | 34 TURING’S THEORy Of mORPHOGENESIS Do Turing patterns exist in nature? Nearly forty years after their existence was first ...

wOOllEy, BAkER, & mAINI | 377 S = 6SS = 8 = 14.4 (a) S = 0.4 S = 1 S = 5 figure 34.2 (a) As the size of the host surface cha ...

378 | 34 TURING’S THEORy Of mORPHOGENESIS Cows, angelfish, and tapirs Why is Turing’s diffusion-driven instability such an attra ...

wOOllEy, BAkER, & mAINI | 379 more problems—and solutions One criticism of Turing’s mechanism is that it often requires a po ...

380 | 34 TURING’S THEORy Of mORPHOGENESIS Although Turing knew that there were limitations to his model, this fortunately did no ...

wOOllEy, BAkER, & mAINI | 381 formulated it. The modern range of experimental and theoretical extensions of his 1952 model s ...