I suppose you could divide 3D space up into vertical lines each crossing the horizontal plane at one point. Then if each of those lines is either all off or all on, the rule will imitate a 2D cellular automaton. In particular, if an alive line has two or three alive neighbours, then each of its cells has 8 or 11 alive neighbours. And if a dead line touches three alive lines, each of its cells has 9 alive neighbours. So B9/S8(11) would simulate life. If you just used very long lines rather than infinite ones then the ends would froth and collapse in, leaving an approximate record of the history of the life universe.

Something something d-brane something holographic principle.

EDIT: I think you need at least B7 or lower in order to have spaceships (Imagine if you were stuck on one side of the plane x+y+z=0 and wanted to get (0,0,0) to turn on). The rule B5 is sort of the equivalent of B3 in two dimensions: B4 and lower explode, so B5 is the first interesting birth rule. I've been playing around with

3DLife.py and it seems like 3D rules are very sensitive. Anything with enough Survival rules to not die out tends to explode.