the fact that both are Turing complete means that, whatever the rules governing the interactions are, for every possible computation there is (at least) a state of the world that performs that computation
Certainly, for an infinite board. But a 3->3->3 board is infinitely smaller than that. What is in question is what portion of universe such as ours can be simulated on such a board...however:
none of these matter
I now agree - with a caveat that one allows arbitrarily long time for the simulation. My earlier remarks were based on an implicit assumption that the computation time for the 2D machine simulating a 3D machine stays constant as the 3D machine size grows.
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.