Some kind of beat and pattern remembering game (the 2x2 12x12 is big enough for simple shapes.

Of course the input isnt ON the array so a simple correllation must exist between the input device and this seperate display.

Another might be a simple maze game where each 12x12 is a window into a larger map and you sequence between 1/2/3/4 (most difficult) different map views in sequence (perhaps all active views have the goal of meeting at some point in the SAME maze)

So you initially explore to get other units in range of each other (blinking ood) and then navigate THEM to come together (once you know they then can spread apart to be becons to get the other views to get to the meeting point.