1. http://en.wikipedia.org/wiki/Hashlife can simulate the Game of Life so fast that it can compute the 6-octillionth generation in 30 seconds. main practitioner: Golly 2. http://rendell-attic.org/gol/tm.htm can be configured to simulate a utm in the Game of Life. goltm.zip\tm.lif webpage in \projects here's another one, probably better: http://www.conwaylife.com/wiki/index.php?title=Spartan_universal_computer-constructor http://myweb.tiscali.co.uk/calcy/life/universal-CC/index.htm projects\*ucc* so, by combining the two, can we create extremely fast universal turing machines? ---- use some of the principles of http://en.wikipedia.org/wiki/Hashlife like caching to improve the speed of a non-game-of-life UTM; whatever algorithm makes it explosively faster is most important. also may be able to simulate different parts of the program at different speeds, but maybe would be an unrelated question to hashlife since cellular automata don't have instruction pointers. but we could give the UTM threading functions. alternatively we could create a cellular automaton (using any rules we like, as long as we can still section-off parts of it) specifically designed to make it easy to emulate a UTM in it. http://en.wikipedia.org/wiki/Memoization