366 | 33 PIONEER Of ARTIfICIAl lIfE
didn’t say that he was already working on a computable theory of how chemicals can guide the
organization of the brain and other bodily structures.
At the time, scant notice was taken of these insights. This is understandable, for they were
presented as mere passing remarks. Moreover, Turing admitted that his 1950 paper offered
no more than ‘recitations tending to produce belief ’, as opposed to ‘convincing arguments of
a positive nature’ about what practical advances might be made in AI and A-Life. By contrast,
his 1952 publication for the Royal Society provided pages of mathematical proof to back up its
startling claims.
An early example of A-Life work, directly inspired by Turing’s ‘mathematical theory of
embryology’, is due to Greg Turk.^27 Turk used a computer to vary the numerical parameters in
Turing’s own equations, to calculate the results, and to apply two or more equations successively
(thus addressing the ‘pattern-from-pattern’ problem that Turing hadn’t solved). In this way,
Turing’s equations have generated spot patterns, stripes, and reticulations resembling those
seen in various living creatures.
Some of the structures produced in these computational experiments are shown in Fig. 33.3.
The large and small spots in the upper half of the picture result from changing the size parameter
in Turing’s reaction–diffusion equation. If the large-spot pattern is frozen and the small-spot
equations then run over it, we get the ‘cheetah spots’ (bottom left). The ‘leopard spots’ (bot-
tom right) are generated by a similar two-step process, except that the numbers representing
the concentrations of chemicals in the large spots are altered before the small-spot equation
is run.
These cascades of reaction–diffusion systems, kicking in at different times, are reminiscent
of the switching on and off of genes, and result in more naturalistic patterns than does a simul-
taneous superposition of the two equations. Similar cascades of a five-morphogen system gen-
erate life-like patterns, and the addition of rules linking stripe equations to three-dimensional
contours produces moulded zebra stripes (Figs 33.4 and 33.5). Of course, the stripes on a real
zebra (or on Blake’s tiger) aren’t quite like these, but this image is more realistic and more
‘natural’ than one showing straight (unmoulded) stripes would be.
figure 33.3 Naturalistic spot patterns.
Reproduced from G. Turk, ‘Generating textures
on arbitrary surfaces using reaction–diffusion’,
Computer Graphics, 25 (1991), 289–98, on p. 292.