| The meaning of the number of states is clear. We
denote this number by S. The interpretation of S is the amount of information
used to describe the contents of each cell. |
| We shall consider mostly binary (S = 2) CA, with states
alive (black) or dead (white). |
| (Von Neumann designed a self-replicating CA with S = 29
states per cell.) |
| Note the number of states per cell is S and the number of cells
making up a neighborhood is N, so there are SN neighborhood
configurations, arrangements of cells in the neighborhood. |
| This is easy to see: |
| * There are S choices of cell states for the first cell in the neighborhood. |
| * Independently of this, there are S choices of cell states for the second cell,
hence there are S2 combinations of states for the first two cells of the
neighborhood. |
| * Continuing, there are S3 combinations of states for the
first three cells of the neighborhood, |
| * ..., |
| * and there are SN combinations
of cells for the neighborhood of N cells. |
| We illustrate these configurations for |
|