@aeva The whole point of the tiling is it forces your hand - you cannot place things where you want - that's why they're aperiodic! So I'm not sure why it's a good thing?

Wang Tiles are the usual way to do random-looking tiling that still obeys edge constraints. That and "wavefront collapse". As usual, fancy names for fairly simple ideas.

If you want spatial locality, plenty of algos use things like Hilbert curves, and that works very well.