Identifying particles [in networks]

In something like a class 4 cellular automaton it is quite straightforward to start enumerating possible persistent structures—as we saw in Chapter 6. But in a network system it can be much more difficult. Ultimately what one wants to do is to find what possible types of forms for local regions are inequivalent under the application of the underlying rules. But in general it may be undecidable even whether two such forms are actually equivalent (compare the notes below and on page 1051)—since to tell this one might need to be able to apply the rules infinitely many times. In specific cases, however, generalizations of concepts like planarity and homotopy may provide useful guides. And a first step may be to look at small closed networks and try to determine which of these can be transformed into each other by a given set of rules.