368 | 33 PIONEER Of ARTIfICIAl lIfE
The more recent Turing-inspired models of biological self-organization go far beyond
Turk’s intriguingly naturalistic spots and stripes, and some of these exemplify the controver-
sial (but increasingly popular) approach known as structuralist biology.^28 The structuralists
insist that Darwinian natural selection is a secondary factor in the explanation of biologi-
cal form—in other words, it merely prunes the forms that have arisen as a result of physics
and chemistry. This implication was not made explicit by Turing, but had been stressed by
D’Arcy Thompson. Many developmental biologists today who draw on Turing’s mathematical
ideas follow Turing in leaving this implication unspoken. (One example is research on what
Turing called ‘leg-evocators’.^29 ) Card-carrying structuralist biologists, however, make a point
of criticizing neo-Darwinism. They argue that physics determines not only what forms are
even possible, but also which are most likely, and so turn up over and over again across the
phylogenetic tree—and they see genes (morphogens) as epigenetic modulators rather than
deterministic instructions.
‘Epigenesis’ is a notion borrowed from the geneticist Conrad Waddington,^30 who was deeply
influenced by D’Arcy Thompson and, like him, was one of the six authors cited in Turing’s 1952
paper. Waddington described development and the activities of genes in terms not of rigidly
pre-defined pathways, but of variable trajectories selected according to the current (ultimately
biochemical) environment. Whereas he, like D’Arcy Thompson, could express this idea in only
the broadest terms, today’s structuralists can do so by using sophisticated experimental data,
advanced mathematics, and the techniques of computer modelling.
For instance, consider the model of the development of the unicellular alga Acetabularia pro-
vided by Brian Goodwin,^31 an ex-pupil of Waddington. This uses computer graphics to present
the numerical results of mathematical calculations as diagrams or pictures of the developing
forms concerned. Like structuralist models in general, it illustrates metabolic and developmen-
tal functions and how they change over time.
Specifically, it simulates the cell’s control of the concentration of calcium ions in the cyto-
plasm, and how this affects, and is affected by, other conditions, such as the mechanical prop-
erties of the cytoplasm, so as to generate one type of morphology or another (such as stalks,
flattened tips, and whorls). It contains some thirty or more parameters, based on a wide range of
experimental work. These reflect factors such as the diffusion constant for calcium, the affinity
between calcium and certain proteins, and the mechanical resistance of the elements of the
cytoskeleton. The model simulates complex iterative feedback loops wherein these parameters
can change from moment to moment.
One welcome result of running this model was the appearance of an alternating pattern
of high and low calcium concentrations at the tip of the stalk (in effect, a modern version of
Turing’s morphogen pattern), interpreted by Goodwin as the emerging symmetry of a whorl.
This result was welcome largely because whorls aren’t found only in Acetabularia: on the con-
trary, they are ‘generic forms’ found in all members of this group of algae and (as Turing himself
had remarked) in many other organisms too.^32 In Goodwin’s model it turned out that whorl
symmetries were very easy to find: they did not depend on a particular combination of specific
parameter values, but emerged if the parameters were set anywhere within a large range of
values.
However, the nature of the computer graphics—whose diagrams were composed of many
tiny lines—prevented the emergence of visually recognizable whorls.^33 A whorl is a crown of
little growing tips, each of which then develops into a growing lateral branch. To simulate this,