My profile image is a constructive proof that all possible dyadic paritionings of a square cannot be enumerated by an algorithm that recursively partitions by halves horizontally or vertically. Any such solution will contain a strut (a line going all the way across), and the image is strutless. In fact, this image illustrates both of the only two strutless solutions when dividing down to 1/4 (ignoring rotations and reflections). I am the sort of person who finds this interesting. ©