Let X be a shape in 2-dimensional space.
Define a square covering of X as a set of axis-aligned squares, whose union exactly equals X.
Note that some shapes don't have a finite square covering, for example, a circle or a triangle.
Define a maximal square covering of X as a square covering where each square is needed, i.e.:
- For every square, there is a point in X that is covered by that square only.
- No two squares can be replaced by a larger square that is contained in X.
Is a maximal square covering, defined in this way, unique? (i.e. can there be two different maximal square coverings of the same shape?)