In general, there is great variety in the possible structures that can be set up in network systems, and as one further example the picture below shows a network that forms a nested pattern.

In the pictures above we have seen various examples of individual networks that might exist at a particular step in the evolution of a network system. But now we must consider how such networks are transformed from one step in evolution to the next.

The basic idea is to have rules that specify how the connections coming out of each node should be rerouted on the basis of the local structure of the network around that node.

But to see the effect of any such rules, one must first find a uniform way of displaying the networks that can be produced. The pictures at the top of the next page show one possible approach based on always arranging the nodes in each network in a line across the page. And although this representation can obscure the geometrical structure

An example of a network that forms a nested geometrical structure. As in all the other networks shown, each node here is identical, and has just two connections coming out of it.

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