There are three very important distinction between "bits contained in our cosmological horizon" and "number of bits contained in 3->3->3 cells" of Conway's life: 2D vs 3D, the complexity of the "rules" governing interaction between the "bits" and the number of possible states of each "bit". This almost certainly (as in "I am very sure, but a formal proof eludes my math skills") means that 3->3->3 cells is far too few to simulate even a small portion of our universe.
I tried for a couple of hours to show this by looking at a number of "natural" states and symbols for a 2D CGoL and possible 3D analogues. I also tried an approach of modelling the growth of a 2D vs 3D machine as a function of computing power. I ran into conceptual difficulties both times, but not before forming an impression that n->n->n notation will be inadequate to compare the two (need to extend to n->n...->n->n... busy beaver, anyone?). Maybe someone with advanced math background can push this further...
2D vs 3D, the complexity of the "rules" governing interaction between the "bits" and the number of possible states of each "bit"
Actually, none of these matter. The possible states of each bit is exactly 2 both for our universe and for (the simplest form) of Life. And 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. This also makes futile the distinction between 2d and 3...
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.