Yet if one only knows constraints then such constraints do not on their own immediately yield any specific procedure for working out what behavior will occur.

But one must realize that a model is only ever supposed to provide an abstract representation of a system—and there is nothing to say that the various elements in this representation need have any direct correspondence with the elements of the system itself.

The growth inhibition mentioned above is a result of the fact that when water or water vapor freezes into ice, it releases a certain amount of latent heat—as the reverse of the phenomenon that when ice is warmed to 0°C it still needs heat applied before it will actually melt. … For being based on traditional mathematical equations they have tended to be able to deal only with what amount to fairly simple smooth shapes—and so have never really been able to address the kind of intricate structure that is so striking in real snowflakes.

In fact, the vast majority of structurally important features seem to have changed only quite slowly and gradually in the course of evolution—just as one would expect from a process of natural selection that is based on smooth variations in fairly simple properties.

The Need for a New Intuition The pictures in the previous section plainly show that it takes only very simple rules to produce highly complex behavior.

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.

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.

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.

The answer is that one has to consider not only the stationary structures that stay in the middle of the system, but also all various small structures that were emitted in the course of the evolution.

And as a result, my guess is that the only realistic way to find the rule in the first place will be to start from some very straightforward representation, and then just to search through large numbers of possible rules in this representation.