This is a modification of Craig S. Kaplan's hatviz application to work as a geomorph-based dungeon generator, similar in concept to Dave's Mapper.
The difference is that the individual geomorphs are the ["hat" tile][hat], from Smith et. al. 2023. Aside from making the maps look a bit weird, this does two things:
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The dungeon maps can never repeat, because the Hat is an aperiodic tile. This isn't super relevant for D&D since we don't usually play on infinite maps, and the details within the geomorphs repeat anyway. But,
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More interestingly, the dungeons have a large-scale structure.
Smith et. al. point out in the paper that the more-commmon non-reflected hat tiles sometimes, but not always, arrange themselves into lines linking the rare reflected tiles.
I've added a blue stripe to the non-reflected tiles that will run along these long-range lines without connecting to the rest of the dungeon. The reflected tiles use different geomorphs, which connect these blue "canal" passages to the rest of the dungeon.
This means adventurers and monsters who want to travel quickly can use the canal system as a shortcut, rather than crawling through the more maze-y dungeon layer. But that also makes canals ideal lairs for the toughest monsters.
This isn't a new idea; the "halls" of Cogmind levels are something similar. But it's not something I've seen as much in D&D maps, possibly because it only really works in quite large dungeons.
To be clear, I'm not affiliated with Kaplan, or any of the "hat" paper authors. I'm just some random who's forked their code to get my geomorph idea working.
The sketch is built using the P5js library. You can run it by pointing your browser at app.html. That file references an online copy of the file. You can also run it with a local copy of the library; download P5.min.js from the P5js download page, put it in the same directory as hat.js and app.html, and modify app.html to reference it instead of the online version.