You absolutely could do that. I think symmetry often looks nice in these things, so you could start to get a bit creative with the algorithm and decide that the

You absolutely could do that. I think symmetry often looks nice in these things, so you could start to get a bit creative with the algorithm and decide that the first 2 bits denote symmetry like {0: None, 1: Vertical Mirror, 2: Horizontal Mirror, 3: 4-fold rotational}. There's a whole tonne of procedural generation tricks you could employ to get interesting aesthetics pretty quickly.