We have already seen with S states per cell and N cells per nbhd, there are SN neighborhood configurations.
A rule specifies exactly which of the S possible states results from each of the SN neighborhood configurations.
Suppose we number the neighborhood configurations 1 through SN.
Then there are S outcomes for configuration 1 and S outcomes for configuration 2, so S2 combinations of outcomes for configurations 1 and 2.
For example, take S = 2, and write the states as 0 and 1. Then the combinations for the first two neighborhood configurations are
Continuing, there are S3 combinations of outcomes for configurations 1, 2, and 3.
For S = 2, here are the combinations for the first three neighborhood configurations
Because there are SN neighborhood configurations,
| there are S(SN) rules. |
How large is this number?
Return to Cellular Automata Basics.