I have posted a previous model of Conway’s Game of Life that runs in Excel – click here to view. I’ve just been reading Daniel Dennet’s book, Freedom Evolves, which uses examples of cellular automata to help describe emergent behaviour. There are some interesting ideas and I’ve been having a play with the Game of Life. For any given point in time the future state is completely determined given the cells that are currently alive and the transition rules of the game. I’ve seeded life with a set of random cells and watch life run over a hundred generations; what is clear is that given the end state there are different ways in which we could have arrived there. In other words I can’t just reverse time and the transition rules to get back to the original state.
One way functions, i.e. easy in one direction and hard in the other, are used to encrypt messages (multiplication vs factoring). We could use the initial state of automata and transition rules to encrypt messages in a computationally inexpensive manner.