Chapter 12: The Principle of Computational Equivalence

Section 6: Computational Irreducibility

More complicated rules [and reducibility]

The standard rule for a cellular automaton specifies how every possible block of cells of a certain size should be updated at every step. One can imagine finding the outcome of evolution more efficiently by adding rules that specify what happens to larger blocks of cells after more steps. And as a practical matter, one can look up different blocks using a method like hashing. But much as one would expect from data compression this will only in the end work more efficiently if there are some large blocks that are sufficiently common. Note that dealing with blocks of different sizes requires going beyond an ordinary cellular automaton rule. But in a sequential substitution system—and especially in a multiway system (see page 776)—this can be done just as part of an ordinary rule.

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