A glider isn’t a cycle. It translates itself. A glider gun isn’t a cycle either, since it creates arbitrarily many gliders. So I think that it’s possible not to end in a cycle in interesting ways as well.
On a higher level, since Life is Turing-complete, it’s perfectly possible that the game state ends in an infinite computation of Pi to higher and higher precision, and never repeats as a result (or, you know, anything else could happen).
A glider isn’t a cycle. It translates itself. A glider gun isn’t a cycle either, since it creates arbitrarily many gliders. So I think that it’s possible not to end in a cycle in interesting ways as well.
On a higher level, since Life is Turing-complete, it’s perfectly possible that the game state ends in an infinite computation of Pi to higher and higher precision, and never repeats as a result (or, you know, anything else could happen).
But GoL on a finite board has only finitely many possible states, and must therefore end up in a cycle.