362 | 33 PIONEER Of ARTIfICIAl lIfE
Turing’s intoxicating paper clearly supplied that ‘smallest beginning’. And although it was only
a beginning, only a seed, it gave very good reason to believe that later work along similar math-
ematical lines would answer a host of questions in embryology, and in developmental biology
in general.
In his thinking about morphogenesis, Turing followed the path that had been pioneered by
the highly original mathematical biologist D’Arcy Thompson:^9 indeed, Thompson’s book On
Growth and Form was one of only six references that he cited.^10 Thompson had insisted that
the most basic aspects of biological form arise because of physics. For instance, a creature like
a water-boatman (an insect that walks on water) has to have bodily dimensions and body parts
that exploit the constraints of surface tension, but its body plan can in effect ignore the force
of gravity. An elephant, by contrast, can forget about surface tension but not about gravity.
(Some parts of its internal organs, of course, may be highly constrained by surface tension; but
Thompson was speaking here of its overall bodily form.) Turing, too, appealed to fundamental
principles of physics and chemistry to explain the origin of form in biology.
In an earlier paper,^11 Turing had already asked how organization could arise in unorganized
neural networks, but there he had assumed some outside interference or training procedure.
Now he considered the origin of organization without outside interference—in other words, the
seemingly paradoxical phenomenon of self-organization. In particular, he asked how homoge-
neous cells can develop into differentiated tissues, and how these tissues can arrange themselves
in regular patterns on a large scale, such as stripes or segments.
Turing didn’t claim to know the chemical details: if the embryologists couldn’t identify the
organizers, neither could he. He spoke of a ‘leg-evocator’, for instance,^12 but that was just a
place-holder for some as-yet-unknown molecule. His achievement was to prove, in mathemat-
ical terms and with the help of computer calculations, that relatively simple chemical processes
could in principle generate biologically relevant order from homogeneous tissue. These pro-
cesses involve chemicals whose mutual interactions as they diffuse throughout the system can
sometimes destroy or build each other.
Since no one knew just which chemicals these might be, Turing referred to them simply as
‘morphogens’. He showed that the interactions between two or more morphogens, each initially
distributed uniformly across the system, could eventually produce waves of differing concen-
trations. This can happen in non-living systems (chemicals diffusing in a bowl, for instance),
as well as in living creatures. But Turing suggested that in an embryo or developing organism a
succession of these processes might prompt the appearance of ordered structures such as spots,
stripes, tentacles, or segments—culminating in the highly differentiated organs of the adult
creature.
This may seem like magic: how can difference arise from homogeneity? Turing allowed that a
perfectly homogeneous system in stable equilibrium would never differentiate. But if the equi-
librium is unstable, even very slight disturbances could trigger differentiation.
As he pointed out, some disturbances are inevitable, given that living matter is subject to
the laws of physics, as D’Arcy Thompson had insisted. For example, random Brownian motion
within the cell fluids must vary the pairwise interactions between the molecules, and molecules
will be slightly deformed as they pass through the cell wall. Even minute disturbances like these
could upset the initial (unstable) equilibrium.
Turing gave differential equations defining possible interactions between two morphogens.
Various terms specified the initial concentrations of the two substances, their rates of diffusion,
the speed at which one could destroy or build up the other, the random disturbances involved,