Have you found that the square proportion or the size of the cards (3"x3") has had any influence on your doodling? The oppression of a white square? 9-square grids?
I find that, in the square format, I tend to create more patterns across the page than isolated compositions. I like squares. They are comfortingly stable and, in an exercise designed to move away from excess analysis and restraint, stability becomes more liberating than stifling.