GART

Multi-scale Truchet

Truchet's tiles, but each square may break into four smaller ones before it decides which way to turn. Arcs still meet at every edge midpoint, so coarse and fine areas join without a break.

Multi-scale Truchet: Truchet's tiles, but each square may break into four smaller ones before it decides which way to turn. Arcs still meet at every edge midpoint, so coarse and fine areas join without a break.Multi-scale Truchet: Truchet's tiles, but each square may break into four smaller ones before it decides which way to turn. Arcs still meet at every edge midpoint, so coarse and fine areas join without a break.

About this pattern

Sébastien Truchet, 1704 · recursive subdivision

Multi-scale Truchet, tessellation, drawn by GART: Truchet's tiles, but each square may break into four smaller ones before it decides which way to turn. Arcs still meet at every edge midpoint, so coarse and fine areas join without a break.
Multi-scale Truchet · CC BY 4.0

The arcs of a Truchet tile always touch the midpoint of all four edges, and that holds whatever size the tile is, so a cell can be quartered and its neighbours never notice. Recursing on that gives a field that is dense in some places and open in others while remaining one continuous maze. Split is the chance that any given square divides rather than settles.

TopicsTessellation (opens in a new tab)Truchet tiles (opens in a new tab)Fractal (opens in a new tab)

Behind the mathematics