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From: Stephen Wolfram, A New Kind of Science
Notes for Chapter 7: Mechanisms in Programs and Nature
Section: Universality of Behavior
Page 967

History [of universality of behavior]. That very different natural and artificial systems can show similar forms has been noted for many centuries. Informal studies have been done by a whole sequence of architects interested both in codifying possible forms and in finding ways to make structures fit in with nature and with our perception of it. Beginning in the Renaissance the point has also been noted by representational and decorative artists, most often in the context of developing a theory of the types of forms to be studied by students of art. The growth of comparative anatomy in the 1800s led to attempts at more scientific treatments, with analogies between biological and physical systems being emphasized particularly by D’Arcy Thompson in 1917. Yet despite all this, the phenomenon of similarity between forms remained largely a curiosity, discussed mainly in illustrated books with no clear basis in either art or science. In a few cases (such as work by Peter Stevens in 1974) general themes were however suggested. These included for example symmetry, the golden ratio, spirals, vortices, minimal surfaces, branching patterns, and - since the 1980s - fractals. The suggestion is also some× made that we perceive a kind of harmony in nature because we see only a limited number of types of forms in it. And particularly in classical architecture the idea is almost universally used that structures will seem more comfortable to us if they repeat in ornament or otherwise forms with which we have become familiar from nature. Whenever a scientific model has the same character for different systems this means that the systems will tend to show similar forms. And as models like cellular automata capable of dealing with complexity have become more widespread it has been increasingly popular to show that they can capture similar forms seen in very different systems.

Stephen Wolfram, A New Kind of Science (Wolfram Media, 2002), page 967.
© 2002, Stephen Wolfram, LLC