presumably somewhere an AI would be created
I would be surprised if only one was created. You would probably get wars going on between the vastly different Artificial Intelligences that arose in there. At some point, one of them would probably "win", although whether we could determine this would depend on whatever it is that particular AI's terminal values were. And of course, it would probably take a really long time.
Conway’s Game of Life is Turing-complete. Therefore, it is possible to create an AI in it. If you created a 3^^3 by 3^^3 Life board, setting the initial state at random, presumably somewhere an AI would be created. Would this AI somehow take over the whole game board, if given enough time?
Would this be visible from the top, as it were?
EDIT: I probably meant 3^^^3, sorry. Also, by generating at random, I meant 50% chance on. But any other chance would work too, I suspect.