Although it is tempting at first to make a version of this Bongard Problem with the solution "Shape can be achieved by folding a square a finite amount of times vs. other shapes", this alternate Bongard Problem would just amount to having the solution "Convex shape with straight edges vs. concave shape or convex shape with at least one curved edge."
Shapes are sorted according to a simple rule that uniquely determines where everything goes vs. shapes are sorted according to some other rule (or lack thereof).