WireWorld Computer
You've probably heard of cellular automata before, at least in the form of Conway's Game of Life. There's another intereating cellular automaton called WireWorld, which performs a model of electrical signal propagation across a grid.
A couple of dedicated souls decided to create a fully-functioning simulated computer in Wireworld. This is a wholly remarkable feat, considering the simplistic nature of Wireworld itself. The computer has another interesting property in that it only has a single instruction, yet is fully Turing-complete thanks to special-purpose registers.