Does the state of a cell in cellular automata has to be from a finite set?
Although Wikipedia mentions a finite set of states (http://en.wikipedia.org/wiki/Cellular_automaton), I'm sure you could find some interesting models that use infinitely many states. As you suggested, each cell could contain an integer, a continuous value between 0 &amp; 1 (shade of grey), etc. 

The idea of basing cell contents upon cell coordinates is interesting and unfamiliar. Of course, you'd have to also include some other inputs in the transition function if you want the pattern to change from step to step. This would create patterns that vary based on their location, which sounds fun to explore.