Taboo 'AI' in your question. Are you looking for: A) A self-modifying structure that contains an internal representation of the surrounding gameboard and a planning algorithm that uses that representation to achieve goals according to some utility function. B) A structure that can pass the Turing test with questions and answers encoded in the game space? C) Something else?
I suspect you meant A. Rephrasing your question gives you an idea what subquestions to look into, such as the degree to which a contained internal representation is possible given the rules of the game and the size of the board.
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.