All possible patterns for a field
Posted: January 20th, 2014, 11:08 pm
(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.
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.