Chapter 8: Implications for Everyday Systems

Section 6: Growth of Plants and Animals

History [of theories of biological form]

The first steps towards a theory of biological form were already taken in Greek times with attempts—notably by Aristotle—to classify biological organisms and to understand their growth. By the 1600s extensive classification had been done, and many structural features had been identified as in common between different organisms. But despite hopes on the part of René Descartes, Galileo and others that biological processes might follow the same kind of rigid clockwork rules that were beginning to emerge in physics, no general principles were forthcoming. Rough analogies between the forms and functions of biological and non-biological systems were fairly common among both artists and scientists, but were rarely thought to have much scientific significance. In the 1800s more detailed analogies began to emerge, sometimes as offshoots of the field of morphology named by Johann Goethe, and sometimes with mathematical interpretations, and in 1917 D'Arcy Thompson published the first edition of his book On Growth and Form which used mathematical methods—mostly from analytical geometry—to discuss a variety of biological processes, usually in analogy with ones in physics. But emphasis on evolutionary rather than mechanistic explanations for a long time caused little further work to be done along these lines. Much additional data was obtained, particularly in embryology, and by the 1930s it seemed fairly clear that at least some aspects of growth in the embryo were controlled by chemical messengers. In 1951 Alan Turing worked out a general mathematical model of this based on reaction-diffusion equations, and suggested that such a model might account for many pigmentation and structural patterns in biological systems (see page 1012). For nearly twenty years, however, no significant follow-up was done on this idea. There were quite a few attempts—often misguided in my opinion—to use traditional ideas from physics and engineering to derive forms of biological organisms from constraints of mechanical or other optimality. And in the late 1960s, René Thom made an important attempt to use sophisticated methods from topology to develop a general theory of biological form. But the mathematics of his work was inaccessible to most natural scientists, and its popularized version, known as catastrophe theory, largely fell into disrepute.

The idea of comparing systems in biology and engineering dates back to antiquity, but for a long time it was mainly thought of just as an inspiration for engineering. In the mid-1940s, however, mostly under the banner of cybernetics, tools from the analysis of electrical systems began to be used for studying biological systems. And partly from this—with much reinforcement from the discovery of the genetic code—there emerged the idea of thinking about biological systems in purely abstract logical or computational terms. This led to an early introduction of 2D cellular automata (see page 876), but the emphasis was on ambitious general questions rather than specific models. Little progress was made, and by the 1960s most work along these lines had petered out. In the late 1970s, however, fractals and L systems (see below) began to provide examples where simple rules could be seen to yield biological-like branching behavior. And in the 1980s, interest in non-equilibrium physical processes, and in phenomena such as diffusion-limited aggregation, led to renewed interest in reaction-diffusion equations, and to somewhat more explicit models for various biological processes. My own work on cellular automata in the early 1980s started a number of new lines of computational modelling, some of which became involved in the rise and fall of the artificial life movement in the late 1980s and early 1990s.

From Stephen Wolfram: A New Kind of Science [citation]