More Cellular Automata
The pictures below show the rules used in the four cellular automata on the facing page. The overall structure of these rules is the same in each case; what differs is the specific choice of new colors for each possible combination of previous colors for a cell and its two neighbors.
There turn out to be a total of 256 possible sets of choices that can be made. And following my original work on cellular automata these choices can be numbered from 0 to 255, as in the picture below.
But so how do cellular automata with all these different rules behave? The next page shows a few examples in detail, while the following two pages [55, 56] show what happens in all 256 possible cases.
At first, the diversity of what one sees is a little overwhelming. But on closer investigation, definite themes begin to emerge.
In the very simplest cases, all the cells in the cellular automaton end up just having the same color after one step. Thus, for example, in