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But there is no need to arrange the picture like this: for the whole behavior of the multiway system can in a sense be captured just by giving the network of what sequence leads to what other. The second set of pictures below shows stages in building up such a network. And what we see is that just as the network systems that we discussed in the previous section can build up their own pattern of connections in space, so also multiway systems can in effect build up their own pattern of connections in time—and this pattern can often be quite complicated.


Evolution of multiway system

The evolution of a multiway system, first with every sequence explicitly shown at each step, and then with every sequence only ever shown once.


Network built by multiway system

The network built up by the evolution of the multiway system from the top of the page. This network in effect represents a network of connections in time between states of the multiway system.

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