Post #2454890

2026-05-09 19:21 UTC

@csk@mathstodon.xyz @tiotasram@kolektiva.social @pieter@mathstodon.xyz I think it only gets to reliable log time in the later articles. In that initial one I think the hat method is still log² in the worst case.

Replies (1)

@tiotasram@kolektiva.social 2026-05-09 22:50

@simontatham@hachyderm.io @csk@mathstodon.xyz @pieter@mathstodon.xyz thanks for the link! I've read through the post and indeed you came up with the same idea of fractal coordinates but for a much harder case (I was applying it to simple squares-in-squares stuff). Advantages that I was interested in which don't apply to your case: you can generate arbitrary patches of the tiling incrementally as a user explores stuff, and you're guaranteed that no matter what path they take, things always match up when they return to somewhere they've been before. So you can do Minecraft-style incremental generation of a huge world and place stuff based on local decisions with logarithmic consultation of higher-level stuff being enough to guarantee aperiodicity, for example. Your idea for sampling from the correct distributions is genius, and it makes me want to try to put together a more "correctly distributed" version of my infinite path demo, although I'll have to think some more about the "correct" distributions of path types through an arbitrary square cutout sampled "uniformly" from all possible infinite Hamiltonian paths through a 1x1 infinite grid.

Open ##2454891