All possible patterns for a field

[tracefleeman]

(if there is anything wrong in these equations, please notify me!)

Let A (out of laziness) be the set of all possible patterns for a field F.

F = A field, some subset of ℤ^n, where n is the dimensionality of a CA
S = The set of states in a CA

A = ℙ(F x S)

For large fields, in which Cartesian products cannot be calculated, let B be the number of patterns for a field F.

B = 2^|F x S|

So, for F = {1,2,3}^2 and S = {0,1}, the number of possible patterns is 262,144.