Here in this simple Wolfram cellalar automaton the cells can take values of 0 or 1.

For transformation to the next generation interesting the state from the left neighbor, the cell itself and the right neighbor. That gives 2^3 = 8 possible states of neighborhood. Every of this 8 neighbourhoods you can dedicate the state 0 or 1. This will be the state for the regarded cell in the next generation. The 8 digits of 0 or 1 can read as a binary number. It gives a distinct transformation rule.

neighbours |
111 |
110 |
101 |
100 |
011 |
010 |
001 |
000 |

state new gen. |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |

This example have the rul 00011110 binary resp. decimal 30. Because of the importance of this rule, GeZA starts with this one in the Wolfram mode.

Another important rule is 110 (decimal). It is proven that rule 110 is an universal Turing machine

With this App you can explore the rules from 0 upto 255.

It is possible to set a memory mode. Here the result will be overruled by a logical operation with the generation before..

ai(t+1) = f(ai-1(t),ai(t), ai+1(t)) XOR ai(t-1)

More information you'll find in the related Wikipedia entry.