The regular tiling by squares can be unfolded by placing hinges at the vertices of tiles, connecting squares to their neighbours. The hinges open continuously to reveal rhombs, which grow into squares and then close up again. The intermediate square tiling offers an opportunity to create an animated loop, but colouring the tiles in that loop so that adjacent tiles never share a colour offers some interesting mathematical challenges. I discuss how many colours are required to permit a looping animation of unfolding squares, and demonstrate a few such loops.