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and (when dealing with multicellular structures) the number and spatial dimensions of the
cells. He showed that certain numerical values of these terms would result in ordered structures
having biological plausibility. For instance, irregular dappling or spot patterns (such as are seen
on dalmatians and some cows) could result from two morphogens diffusing on a plane surface
(Fig. 33.1).
As another example, diffusion waves of two morphogens within a twenty-cell ring could give
rise to regularly spaced structure, reminiscent of the embryonic beginnings of circular patterns
of cilia, tentacles, leaf buds, or petals—or segments, if the ring were broken. Three developmen-
tal stages within this twenty-cell body are represented in Fig. 33.2: the initial homogeneous
equilibrium (dotted line), early signs of an emerging pattern (hatched line), and the final equi-
librium (unbroken lines).
Turing suggested that order could be generated in three dimensions also. For example, dif-
fusion waves could cause embryonic gastrulation, in which a sphere of homogeneous cells
develops a hollow (which eventually becomes a tube), and interactions between more than
two morphogens could produce travelling waves, such as might underlie the movements of a
spermatozoon’s tail.
There were two reasons why he focused on the origin of form from a homogeneous source.
One was that this is the most fundamental (and therefore the most puzzling) case. The second
0.50123456789 10 11 12 13 14 15 16 17 18 191.01.5figure 33.2 Concentrations of a morphogen
diffusing in a twenty-cell ring. This picture was also
drawn by Turing, but represents calculations so
taxing that they had to be done on the Manchester
computer;^13 that was why (as remarked earlier)
he had awaited the delivery of the machine so
impatiently.
Reproduced from A. M. Turing, ‘The chemical basis of
morphogenesis’, Philosophical Transactions of the Royal
Society (B), 237 (1952), 37–72, on p. 60.figure 33.1 Dappling produced by diffusion
equations; this picture was hand-drawn by Turing,
on the basis of numerical calculations done using
his desk calculator.
Reproduced from A. M. Turing, ‘The chemical basis of
morphogenesis’, Philosophical Transactions of the Royal
Society (B), 237 (1952), 37–72, on p. 60.