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grow by splitting off smaller stems. And indeed it is even known that some of the genetic phenomena involved are extremely similar.

But the point is that because of the comparative rigidity of plants during their most important period of growth, only structures that involve fairly explicit branching can be produced. In animals, however, the lack of rigidity allows a vastly wider range of structures to appear, since now tissue in different regions need not just grow uniformly, but can change shape in a whole variety of ways.

By the time an animal hatches or is born, its basic form is usually determined, and there are bones or other rigid elements in place to maintain this form. But in most animals there is still a significant further increase in size. So how does this work?

Some bones in effect just expand by adding material to their outer surface. But in many cases, bones are in effect divided into sections, and growth occurs between these sections. Thus, for example, the long bones in the arms and legs have regions of growth at each end of their main shafts. And the skull is divided into a collection of pieces that each grow around their edges.

Typically there are somewhat different rates of growth for different parts of an animal—leading, for example, to the decrease in relative head size usually seen from birth to adulthood. And this inevitably means that there will be at least some changes in the shapes of animals as they mature.

But what if one compares different breeds or species of animals? At first, their shapes may seem quite different. But it turns out that among animals of a particular family or even order, it is very common to find that their overall shapes are in fact related by fairly simple and smooth geometrical transformations.

And indeed it seems likely that—much like the leaves and shells that we discussed earlier in this section—differences between the shapes and forms of animals may often be due in large part merely to different patterns in the rates of growth for their different parts.

Needless to say, just like with leaves and shells, such differences can have effects that are quite dramatic both visually and mechanically—turning, say, an animal that walks on four legs into one that walks on

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