Examples of networks determined by constraints. In each case the networks shown are required to satisfy the constraint that around every node their form must correspond to the template shown, in such a way that no dangling connections in the template are joined to each other. The pictures include all 14 templates that involve nodes out to distance at most two for which complete networks can be formed. In most cases where any such network can be formed, an infinite sequence of networks is allowed. But in cases (b), (h), (i) and (j) just a single network turns out to be allowed. The network constraint systems shown here are analogs of the two-dimensional systems based on constraints discussed at the end of Chapter 5.

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