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Note that a single connection can join events that occur at very different steps in the evolution of the underlying mobile automaton. And indeed to construct even a small part of the causal network can require an arbitrarily long computation in the underlying mobile automaton. Thus for example to make the causal networks in pictures (e), (f) and (g) requires looking respectively at 2447, 731 and 322 steps of mobile automaton evolution. And indeed in some cases there can be connections that are in effect never resolved. And thus for example in picture (a) there are downward connections that never reach any other node—reflecting the presence of positions on the left in the mobile automata evolution to which the active cell never returns.

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