Truchet Tiling: From 1704 to Infinite Patterns
How a Dominican friar's observation about ceramic tiles became one of the most elegant combinatorial systems in decorative mathematics — and how Patchwork lets you explore it.
A friar in a tile workshop
In 1704, Sébastien Truchet, a French Dominican friar with a remarkable gift for combining mathematics and craftsmanship, visited a factory in the village of Marly. There he encountered square ceramic tiles, each divided diagonally into two contrasting colored triangles. Truchet noticed something delightful: placing just two identical tiles side by side in different orientations could produce an enormous variety of geometric figures.
He catalogued all non-equivalent ways to combine pairs of these tiles, producing 64 combinations. His work, 'Mémoire sur les combinaisons,' was published in 1722 by Dominique Douat, who extended Truchet's observations and systematically explored what happens when the tiles tile the plane.
The four original tiles
Truchet's system rests on a single tile with four possible orientations — rotations of 90° each. The diagonal divides the square into a dark triangle and a light triangle. From this single shape, all the complexity emerges:
Like the classic examples, the same tile can produce an orderly scheme or a random placement:
Smith's curved simplification (1987)
Nearly three centuries later, historian of materials science Cyril Stanley Smith revisited Truchet tiling in his 1987 article 'The tiling patterns of Sebastien Truchet and the topology of structural hierarchy.' Smith's curved tile is not the generic one-corner quarter-circle often shown in Truchet examples: it carries two quarter-circle arcs at opposite corners, so all four edge midpoints are connected.
This small change has a dramatic visual effect. Where the original Truchet tiles produce angular geometric patterns, Smith's paired arcs generate flowing labyrinthine forms — paths that wind continuously across the plane without ever crossing themselves. Patchwork uses the two true Smith arc orientations.
In random placement, the two orientations create continuous maze-like curves. The same placement can be rendered as curved arcs, as Smith's straight double-band variant, or as the single-diagonal labyrinth form:
Why the randomness works
The Smith arc and double-band forms have only two states, but each state connects all four edge midpoints: top to one side and bottom to the other, in opposite pairings. Because every edge midpoint still meets a midpoint in the neighboring square, random choices do not break the drawing. They change the routing of the continuous curves. The single-diagonal version works differently: it leaves separated walls and corridors, producing the classic diagonal Truchet labyrinth.
Create your own patterns
One of the remarkable properties of Truchet tiling is that even a random arrangement of tiles (each orientation chosen by coin-flip) produces a visually coherent pattern. There is no 'wrong' placement — every configuration is interesting. This makes it an ideal generative design system: the rules are minimal, but the output space is vast.
Patchwork gives you Truchet's diagonal tiles and Smith's paired arc tiles, plus many more related block families, with full control over color, layering, and composition. Open the app and explore: pick the diagonals or the Smith arcs from the tile panel and start placing them on the canvas.
Open Patchwork and start tilingMathematical properties
Truchet tilings belong to a class of aperiodic-capable tilings — configurations that can fill the plane without repeating in a strict periodic pattern. Unlike a regular grid, a random Truchet tiling has no translational symmetry: you cannot shift the entire pattern by any fixed vector and have it look the same. This makes Truchet tilings useful in cryptography, texture generation, and generative art, where non-repetition is a virtue.