Indeed, it is a general feature of class 4 cellular automata that with appropriate initial conditions they can mimic the behavior of all sorts of other systems. And when we discuss computation and the notion of universality in Chapter 11 we will see the fundamental reason this ends up being so. But for now the main point is just how diverse and complex the behavior of class 4 cellular automata can be—even when their underlying rules are very simple.

And perhaps the most striking example is the rule 110 cellular automaton that we first saw on page 32. Its rule is extremely simple—involving just nearest neighbors and two colors of cells. But its overall behavior is as complex as any system we have seen.

The facing page shows a typical example with random initial conditions. And one immediate slight difference from other class 4 rules that we have discussed is that structures in rule 110 do not exist on a blank background: instead, they appear as disruptions in a regular repetitive pattern that consists of blocks of 14 cells repeating every 7 steps.

The next page shows the kinds of persistent structures that can be generated in rule 110 from blocks less than 40 cells wide. And just like in other class 4 rules, there are stationary structures and moving structures—as well as structures that can be extended by repeating blocks they contain.

So are there also structures in rule 110 that exhibit unbounded growth? It is certainly not easy to find them. But if one looks at blocks of width 41, then such structures do eventually show up, as the picture on page 293 demonstrates.

So how do the various structures in rule 110 interact? The answer, as pages 294296 demonstrate, can be very complicated.

In some cases, one structure essentially just passes through another with a slight delay. But often a collision between two structures produces a whole cascade of new structures. Sometimes the outcome of a collision is evident after a few steps. But quite often it takes a very large number of steps before one can tell for sure what is going to happen.

So even though the individual structures in class 4 systems like rule 110 may behave in fairly repetitive ways, interactions between these structures can lead to behavior of immense complexity.

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