In Conway's game of life, take the initial position to be two infinite diagonal lines of live cells, with a single cell in common. Does this thing converge to a stable configuration? I.e., is the state of each cell (or finite region) eventually periodic?
Added the infinite games tag as i understand there is an initiative for this tag. i'll restrict my tagging only to questions where i have no uncertainty, so long as that's ok with the community. it's really useful for me to review these questions.