Tiles manipulates an array of cells, each of which is either a square, two triangles separated by a bend dexter, or two triangles separated by a bend sinister. But instead of showing you these shapes, Tiles displays their dual. Relatively simple patterns in shape space (the dual of the space you’re seeing) have duals that are all squares, octagons mingled with squares, and, amazingly, a tiling of the plane with (irregular, of course) pentagons.
An ancient MacOS implementation that offers more features is available here