Cellular automata are much harder to screw around with. Partly that is because computation by hand is a lot harder, partly because there isn't much that one can

Cellular automata are much harder to screw around with. Partly that is because computation by hand is a lot harder, partly because there isn't much that one can combine. What makes the integers interesting is that addition, multiplication and exponentiation are all easy, all operate on the same numbers, and yet they behave very differently. This allows one to pose very easy questions (e.g. Can I express every prime as a sum of ...) that have no obvious solution to them.