In a cellular automaton of limited size n , any column must eventually repeat.

• Is there an initial condition to a cellular automaton that yields particular behavior after a given number of steps?

For it is almost certain that experiments on, say, some specific cellular automaton whose rule has been picked at random from a large set will never have been done before.

(Even if one can do operations on all digits in parallel it still takes of order n steps in a system like a cellular automaton for the effects of different digits to mix together—though see also page 1149 .)

But it is not uncommon for them to be used—like in a cellular automaton—as a way of specifying how structures should be built up. … (Go involves putting black and white stones on a grid, making it visually similar to a cellular automaton.)

It was noted that both very ordered and very disordered systems normally seem to be of low complexity, and much was made of the observation that systems on the border between these extremes—particularly class 4 cellular automata—seem to have higher complexity. … Following my 1984 study of minimal sizes of finite automata capable of reproducing states in cellular automaton evolution (see page 276 ) a whole series of definitions were developed based on minimal sizes of descriptions in terms of deterministic and probabilistic finite automata (see page 1084 ).

These tests mostly seem simpler than those shown on page 597 obtained by running a cellular automaton rule on the data.

For example, one can imagine not just forming a ball on the network, but instead growing something like a cellular automaton, and seeing how big a pattern it produces after some number of steps.

And even though for example elaborate symmetry rules have been devised, nothing like cellular automaton rules appear to have ever arisen. … The triangles are all equilateral, with the result that at a given step several different sizes of triangles occur—though the basic structure of the pattern is still the same as from the rule 90 cellular automaton.

The first 2 m elements in the sequence can be obtained from (see page 1081 ) (CoefficientList[Product[1 - z 2 s , {s, 0, m - 1}], z] + 1)/2 The first n elements can also be obtained from (see page 1092 ) Mod[CoefficientList[Series[(1 + Sqrt[(1 - 3x)/(1 + x)])/ (2(1 + x)), {x, 0, n - 1}], x], 2] The sequence occurs many times in this book; it can for example be derived from a column of values in the rule 150 cellular automaton pattern discussed on page 885 .