I was recently reading about artificial life and came across the statement, \"Conway’s Game of Life demonstrates enough complexity to be classified as a universal machine.\"
You can build a Turing machine out of Conway's life - although it would be pretty horrendous.
The key is in gliders (and related patterns) - these move (slowly) along the playing field, so can represent streams of bits (the presence of a glider for a 1 and the absence for a 0). Other patterns can be built to take in two streams of gliders (at right angles) and emit another stream of bits corresponding to the AND/OR/etc of the original two streams.
EDIT: There's more on this on the LogiCell web site.