0 · Compare the two exponent tests

An exponent controls both the shape of the unit region and the effect of merging boxes. Convexity and stable merging are different conditions, although both change at exponent one.

Try this. Move the exponent through one. Below one, the unit region is not convex, but merging no longer increases the size. Read both results before deciding which condition has passed.

For n equal boxes, the merge ratio is n raised to one minus the reciprocal of the exponent. The browser evaluates this formula, and the Python tests check both the ratio and the convexity result.