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And what we have found in this book is that programs are very much the same: some show highly complex behavior, while others show only rather simple behavior.
Experience with systems from hand-held objects to engineering structures and earthquakes suggests that it can take a while for a crack to get started, but that once it does, the crack tends to move quickly and violently, usually producing a lot of noise in the process.
And in the case where there is very little damping the last two pictures show that at least for a while elements can form at fairly random angles.
And while the positions of particular updating events are different in every picture, the point is that the network of causal connections between these events is always exactly the same.
Typically properties like charge will be associated with some specific pattern of connections at the core of the structure corresponding to a particle, while the energy and momentum of the particle will be associated with roughly the number of nodes in some outer region around the core.
And if there is a fixed such scheme, then this implies that while certain similarities between pieces of data will immediately be recognized, others will not.
Similarly, rule 62 can be thought of as enumerating numbers that are multiples of 3, while rule 190 enumerates numbers that are multiples of 4.
less computational sophistication than is implied by the principle, while others will be based on believing that they have more.
But while we found that such behavior is quite common in cellular automata, what we have seen in this section indicates that it is rather rare in mobile automata.
For while simple infinite quantities like 1/0 or the total number of integers can readily be summarized in finite ways—often just by using symbols like ∞ and ℵ 0 —the same is not in general true of all infinite processes.