Note (j) for More Cellular Automata…[Cellular automata with] two-cell neighborhoods By having cells on successive steps be arranged like hexagons or staggered bricks, as in the pictures below, one can set up cellular automata in which the new color of each cell depends on the previous colors of two rather than three neighboring cells. … For k = 2 , there are 16 possible rules, and the most complicated pattern obtained is nested like the rule 90 elementary cellular automaton.

Features of the [patterning] model The model is a totalistic 2D cellular automaton, as discussed on page 927 . … And following my work on cellular automata in the early 1980s, David Young in 1984 considered a model even more similar to the one I use here. There are simple cellular automata—such as 8-neighbor outer totalistic code 196623—which eventually yield maze-like patterns even when started from simple initial conditions.

These operations can be thought of as finding elements in nested Pascal's triangle patterns produced by k -color additive cellular automata. Korec showed that finding elements in the nested pattern produced by the k = 3 cellular automaton with rule {{1, 1, 3}, {2, 2, 1}, {3, 3, 2}} 〚 #1, #2 〛 & (compare page 886 ) was also enough.

Code 10 Rule 30 is by many measures the simplest cellular automaton that generates randomness from a single black initial cell.

The picture on the next page shows a two-dimensional cellular automaton where this happens. … In discussing two-dimensional cellular automata in Chapter 5 , for example, we saw many examples where randomness occurs, but where the overall forms of growth that are produced have a complicated structure with no particular smoothness or continuity.

But the rule 30 cellular automaton that we discussed above demonstrates that in fact this is absolutely not the case.

Patterns produced by taking a single black cell, then evolving for 50 and 100 steps according to outer totalistic cellular automaton rules 54, 222 and 374.

And as I discussed in the previous chapter the process of evolution of a system like a cellular automaton can for example perfectly well be viewed as a computation, even though in a sense all the computation does is generate the behavior of the system.

The system that I looked at was a 2D cellular automaton with discrete particles colliding on a square grid.

A cellular automaton model can be made by allowing particles with more than one possible energy: the average particle energy in a region corresponds to fluid temperature.