I think I know what you mean. I downloaded something called "Magic Squares" for my HP 48GX calculator a few years ago. I was playing with the idea on that one too, but I would have to flip/rotate identical screens just to get it to fit. I believe that one could be made, similiarly to the tic-tac-toe.

The one for the calculator started with a random screen. The trick would be to getting a "random" start screen, but I may use George's idea for that, just start with one of 4 starting sequences.