How to define two 2D fields projecting onto one another

Let's say you have two continuous 2D fields which can take on some activity (which can be different from each other), now say that activity can spread between the two fields, but only through corresponding locations (e.g. field x at point (3,1) can excite field y at point (3,1) and vice versa), how would you define that space that is created? Is it a fractional dimension (because it is a discrete number of continuous spaces)? Any help conceptualizing would be very appreciated.