particular rule, then one will always eventually be able to find a set of localized structures that is rich enough to support universality. The final demonstration that a given rule is universal will no doubt involve the same kind of elaborate construction as for rule 110. … I strongly suspect that all class 4 rules, like rule 110, will turn out to be universal.

But if the ultimate rule for the universe is at all simple, then it follows that every part of this rule must in a sense be responsible for a great many different features of the universe. … So this means that one cannot reasonably expect to use some kind of incremental procedure to find the ultimate rule for the universe. But it also means that if one once discovers a rule that reproduces sufficiently many features of the universe, then it becomes extremely likely that this rule is indeed the final and correct one for the whole universe.

Rule 4 picks out isolated black cells. Rule 60 essentially constructs a difference table for the sequence of elements. Rules 57 and 184 test for the overall density of black cells.

[No text on this page] The universal cellular automaton emulating elementary rule 90. The underlying rules for the universal cellular automaton are exactly the same as on the previous page . But each block in the initial conditions now contains a representation of rule 90 rather than rule 254.

And with rule (b), obvious repetitive behavior is obtained. … It turns out that even with rule (c), which is essentially just a combination of rules (a) and (b), significantly more complicated behavior can already occur. … More steps in the evolution of rule (c) from the previous page .

But it turns out that with slightly more complicated rules it is possible to get much more complicated behavior. … Examples of sequences generated by rules that do not depend only on elements a fixed distance back. Most such rules eventually end up involving meaningless quantities such as f[0] and f[–1] , but the particular rules shown here all avoid this problem.

rules 0 and 128 all the cells become white, while in rule 255 all of them become black. … Sometimes this pattern remains stationary, as in rules 4 and 123. … And in many rules, this maximum speed is achieved—although in rules such as 3 and 103 the average speed is instead only half a cell per step.

But by changing the rule slightly, one can obtain more complicated patterns of growth. … (In the numbering scheme described on page 173 this rule is code 1022.) … (In the numbering scheme on page 173 , the rule is code 942.)

In the second case rule 73 exhibits typical class 3 behavior—with the usual uncontrolled transmission of information. … And while these structures may at first seem more like those in rule 54 than rule 110, I strongly suspect that the complexity of the typical behavior of rule 73 will be reflected in more sophisticated interactions between the structures—and will eventually provide what is needed to allow universality to be demonstrated in much the same way as in rule 110. Two examples of rule 73.

But why should we believe that the rule for our universe is in fact simple? Certainly among all possible rules of a particular kind only a limited number can ever be considered simple, and these rules are by definition somehow special. … Yet we know, I think, that the rule for our universe is not too complex.