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application of three-dimensional geometry to very simple underlying rules of growth. And so once again therefore natural selection cannot reasonably be considered the source of the elaborate forms we see.

Away from mollusc shells, coiled structures—like branched ones—are not especially common in animals. Indeed, the vast majority of animals do not tend to have overall forms that are dominated by any single kind of structure. Rather, they are usually made up of a collection of separate identifiable parts, like heads, tails, legs, eyes and so on, all with their own specific structure.

Sometimes some of these parts are repeated, perhaps in a sequence of segments, or perhaps in some kind of two-dimensional array. And very often the whole animal is covered by a fairly uniform outer skin. But the presence of many different kinds of parts is in the end one of the most obvious features of many animals.

So how do all these parts get produced? The basic mechanism seems to be that at different places and different times inside a developing animal different sections of its genetic program end up getting used—causing different kinds of growth to occur, and different structures to be produced. And part of what makes this possible is that particularly at the stage of the embryo most cells in an animal are not extremely rigid—so that even when different pieces of the animal grow quite differently they can still deform so as to fit together.

Usually there are some elements—such as bones—that eventually do become rigid. But the crucial point is that at the stage when the basic form of an animal is determined most of these elements are not yet rigid. And this allows various processes to occur that would otherwise be impossible.

Probably the most important of these is folding. For folding is not only involved in producing shapes such as teeth surfaces and human ear lobes, but is also critical in allowing flat sheets of tissue to form the kinds of pockets and tubes that are so common inside animals.

Folding seems to occur for a variety of reasons. Sometimes it is most likely the direct result of tugging by microscopic fibers. And in other cases it is probably a consequence of growth occurring at different rates in different places, as in the pictures on page 412.

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