It reminds me of a technique for using recursive self-similar tiles to generate pseudorandomly distributed points: http://johanneskopf.de/publications/blue_noise/

The idea is that you can model an infinite set of points generated by an infinitely-deeply-nested tiling, and then efficiently sample from it at arbitrary levels of detail. This lets you do things like zoom in and out while retaining frame-to-frame coherence, and without having to explicitly store the entire point set. (It's worth watching the full 5-minute video, which explains it better than I can.)

The implementation in that paper used squares with labeled edges to tile the plane non-periodically. This seems like it could be used to do something similar, except with a periodic but irregular tiling. No idea if that would have any practical benefits, but it's interesting, at least.

Bathrooms?

There need not be. 1+1=2 is true whether we are adding dollars or lines of code. Another answer is that I'm trying to make a puzzle with different solutions, all of which can't be solved simultaneously.

My first thought was for tiled textures, to make repetition less obvious

https://en.wikipedia.org/wiki/Digital_camouflage ?

I think that depends on the world you're trying to apply it to.