Conway's Game of Life is a well-known cellular automaton in which, every tick, the state of each of the cells on a giant grid is determined only by the states of its immediate neighbours in the previous tick. Despite its extremely simple definition, it is famously Turing-complete, which is roughly to say that it can compute any computable function.
And so, of course, someone has written a Life emulator, in Life.
Perhaps it's Life all the way down...