Reading the Wikipedia entry on Conway's Game of Life answers the question of why it was developed "Conway was interested in a problem presented in the 1940s by renowned mathematician John von Neumann, who tried to find a hypothetical machine that could build copies of itself and succeeded when he found a mathematical model for such a machine with very complicated rules on a rectangular grid." It's interesting that von Neumann's idea of self replication actually predates the discovery of DNA by a few years.
So I asked Google the question and someone has implemented a Turing machine inside Coway's Game of Life; way back in 2000. A book called "Collision Based Computing" and a applet called LogiCell (which uses Conway's Game of Life to do simple calculations) is available here.
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