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typically spreads at a uniform rate, eventually affecting every part of the system. In class 4, changes can also spread, but only in a sporadic way—as illustrated on the facing page and the one that follows.

So what is the real significance of these different responses to changes in initial conditions? In a sense what they reveal are basic differences in the way that each class of systems handles information.

In class 1, information about initial conditions is always rapidly forgotten—for whatever the initial conditions were, the system quickly evolves to a single final state that shows no trace of them.

In class 2, some information about initial conditions is retained in the final configuration of structures, but this information always remains completely localized, and is never in any way communicated from one part of the system to another.

A characteristic feature of class 3 systems, on the other hand, is that they show long-range communication of information—so that any change made anywhere in the system will almost always eventually be communicated even to the most distant parts of the system.

Class 4 systems are once again somewhat intermediate between class 2 and class 3. Long-range communication of information is in principle possible, but it does not always occur—for any particular change is only communicated to other parts of the system if it happens to affect one of the localized structures that moves across the system.

There are many characteristic differences between the four classes of systems that we identified in the previous section. But their differences in the handling of information are in some respects particularly fundamental. And indeed, as we will see later in this book, it is often possible to understand some of the most important features of systems that occur in nature just by looking at how their handling of information corresponds to what we have seen in the basic classes of systems that we have identified here.

Captions on this page:

The effect of small changes in initial conditions in the rule 110 class 4 cellular automaton. The changes spread only when they are in effect carried by localized structures that propagates across the system.

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