Where it shows up
Sébastien Truchet catalogued these tilings in 1704 while studying how a single two-tone square could be combined, and the trick keeps resurfacing. Maze generators lean on it for cheap, guaranteed-connected corridors. Circuit-board and pipe-routing art use the arc tile to fake plausible plumbing. The same "constrain the boundary, free the interior" principle drives Wang tiles, procedural texture synthesis, and the aperiodic monotile hunt that produced the hat in 2023. Even knitting and Islamic tilework reach for it: decide a rule at the edges and let the middle roll freely, and coherence comes for nothing.
The knobs
- Tiles across: how many cells span the width. Fewer means big bold arcs; more means a fine, dense weave. Changing it re-seeds the field.
- Motif: swap the tile. Arcs for flowing loops, Diagonals for a hard-edged maze, Triangles for a filled mosaic.
- Reseed wave: how fast the diagonal wavefront advances. At zero the pattern freezes; wind it up and the field churns continuously.
- Line width: stroke weight for arcs and diagonals, and the width of the background grout seams between triangles.