Picture (b) is very similar to (a), but shows successive steps of mobile automaton evolution separated, with gray blobs in between indicating "updating events" corresponding to each application of the underlying mobile automaton rule.

The rules for such cellular automata work by assigning to each possible neighborhood of cells a certain probability to generate a cell of each color.

The interior of the pattern that emerges is like an inverted version of the rule 60 additive cellular automaton; the boundary, however, is more complicated.

For given the state of a system, they provide rules for determining its state at subsequent times.

For the particular rules shown it is fairly easy to demonstrate that there are never inconsistencies.

And if one assumes consistency then it follows that there must be strings where neither the string nor its negation can be The effect of adding transformations to the rules for a multiway system.

The rule diagrams in this book represent a possible new method for specifying some simpler programs, but it remains to be seen whether such diagrams can readily both be created incrementally by humans and interpreted by computer.

Most schemes like this can ultimately be thought of as picking out templates or applying simple cellular automaton rules.

Conway considered fraction systems based on rules of the form FSEvolveList[fracs_, init_, t_] := NestList[First[Select[fracs #, IntegerQ, 1]] &, init, t] With the choice fracs = {17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/ 23, 77/19, 1/17, 11/13, 13/11, 15/14, 15/2, 55/1} starting at 2 the result for Log[2, list] is as shown below, where Rest[Log[2, Select[list, IntegerQ[Log[2, #]] &]]] gives exactly the primes.

However, as noticed by John Conway around 1986, the sequences can actually be obtained by a neighbor-independent substitution system, acting on 92 subsequences, with rules such as {3, 1, 1, 3, 3, 2, 2, 1, 1, 3}  {{1, 3, 2}, {1, 2, 3, 2, 2, 2, 1, 1, 3}} .