Given a grid representing a state in Conway's game of life, if there is no pattern that leads to this state, this means that there exists a forbidden $N\times N$ pattern for some $N$.
If so what is the smallest $N$ such that an $N\times N$ pattern is forbidden? i.e. that it can't exist as a subregion of a next step of a state?
In other words, given all possible states (on a massive grid), evolve them by one time step. Find the smallest $N\times N$ pattern that never occurs. What is $N$? I think it will be as small as 3,4 or 5.
e.g. I think it might be unlikely that a $5\times 5$ pattern where each cell is 'alive' would be in any time step of the game of life (except possibly for the initial state). But I can't prove it.