typical animal embryo they at first seem remarkably haphazard. But presumably the main thing that is going on—as mentioned above—is that at different places and different times different sections of the underlying genetic program are being used, and these different sections can lead to very different kinds of behavior. Some may produce just uniform growth. Others may lead to various kinds of local folding. And still others may cause regions of tissue to die—thereby for example allowing separate fingers and toes to emerge from a single sheet of tissue.

But just how is it determined what section of the underlying genetic program should be used at what point in the development of the animal? At first, one might think that each individual cell that comes into existence might use a different section of the underlying genetic program. And in very simple animals with just a few hundred cells this is most likely what in effect happens.

But in general it seems to be not so much individual cells as regions of the developing animal that end up using different sections of the underlying program. Indeed, the typical pattern seems to be that whenever a part of an animal has grown to be a few tenths of a millimeter across, that part can break up into a handful of smaller regions which each use a different section of the underlying genetic program.

So how does this work? What appears to be the case is that there are cells which produce chemicals whose concentrations decrease over distances of a few tenths of a millimeter. And what has been discovered in the past decade or so is that in all animals—as well as plants—there are a handful of so-called homeobox genes which seem to become active or inactive at particular concentration levels and which control what section of the underlying genetic program will be used.

The existence of a fixed length scale at which such processes occur then almost inevitably implies that an embryo must develop in a somewhat hierarchical fashion. For at a sufficiently early stage, the whole embryo will be so small that it can contain only a handful of regions that use different sections of the genetic program. And at this stage there may, for example, be a leg region, but there will not yet be a distinct foot region.

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