It's ok if your problem does not meet the strict definition of being in NP, as long as it has the same form: a yes/no problem such that a yes answer means that there is some kind of solution which can be quickly checked for correctness, even though it might be difficult to find the solution.
(Note that this is the opposite direction of translation from what you would use to prove your problem NP-complete.)
Input: numbers W,L,S,P.
Output: "yes" if there exists a pattern that repeats itself P generations after the start, shifted over by S steps, and that fits within a W*L rectangle.
To check a solution, simply compute the evolution of the pattern for P steps, and compare the result with a shifted copy of the original pattern. (This problem is not actually in NP, because the input size is so small that even writing down a solution is exponential in the input size.)
Form a binary variable for each pair (c,t), where c is a cell in the W*L rectangle and t is a time step from 0 to P-1. Form a constraint for each such variable, saying that the variable should match the result of evolving the nine neighboring cells in time step (t-1), or (if t=0) that it should match the result of evolving the nine cells surrounding the point S steps away from its position in step P-1. Also add one more constraint, that at least one cell is nonempty.