> future states that all contain the same specific pattern.
Past yes, but probably not future surely? I see no reason such a pattern couldn't be broken by outside influence somewhere in the future.
Past yes, but probably not future surely? I see no reason such a pattern couldn't be broken by outside influence somewhere in the future.
A Conway's Life pattern that has to stay the same into the indefinite future would be an impenetrable wall, and we don't know of any such thing in the Life rule. It hasn't exactly been proved impossible, but nobody seriously thinks that such a thing exists.
I think it _can_ easily be proven that a finite stable (period 1) impenetrable wall can't exist. It's trivial to find a way to attack the corners, and almost equally trivial to find something that makes a change at any edge.