The obvious issue is that the topology is full of loops, so making the curve handle them is tricky. And the 6-triangle hexagonal building blocks need the right entry and exit rules (here ChatGPT was trying a Gosper snake relative), with chirality mattering.
Anders Sandberg@anderssandberg
Here is a fun little problem: how to generalise a plane-filling curve to cover the gyroid minimal surface. The fundamental patch is the (2,4,6) triangle tiling of the hyperbolic plane, so classic Hilbert is out. (Claude did a brave attempt, but lacks geometric "seeing")
8:40 AM · Jun 16, 2026 · 329 Views