# Does the state of a cell in cellular automata has to be from a finite set?

In most (all I have seen) work on cellular automata, the state of a cell is from a finite set. Such as a cell can take value from a binary set, or from among few colors. Can we define the state to be something more complicated such as a function of the coordinates of the neighbor cells? (assuming there is a initial coordinate value give to at least one cell) So for example in 2-D if my neighbor to the left has coordinate $(x,y)$ my state will take a value $f(x,y)$ where $f$ is same for all cells.

• Does your function $f$ depend in any way on the contents of the cells? – Yuval Filmus Feb 14 '14 at 21:51
• You are asking two different questions: (1) Does the "cell alphabet" have to be finite? (2) Can the "transition function" depend on the coordinates? In both cases, you have to be careful about $f$: it should be computable. I don't know if these models have ever been studied. – Yuval Filmus Feb 14 '14 at 21:52
• @YuvalFilmus $f$ depends on the coordinates of the neighbors and of the cell itself. So the color of the cell, I believe that is what you mean by cell alphabet, is given by $f$ and it is not a finite set. – Mat Feb 15 '14 at 16:09