Sébastien Truchet1657–1729
The divided square, 1704
French mathematician whose 1704 study showed how rotations of one divided square could generate remarkably varied ornamental fields.
Truchet Triangles
The original Truchet tile: a square cut on its diagonal, one half dark. Four turns of it, arranged by rule, give diamonds, chevrons and pinwheels.
About this pattern
Sébastien Truchet, 1704 · Dominique Douat, 1722
Truchet's 1704 memoir began with a square split corner to corner into two coloured triangles, and asked how many patterns its four rotations could make. Douat answered in 1722 with a method: fix a small block of tiles, then fill the plane with copies of that block mirrored or turned by a rule, which is how the diagonal square became a pattern language rather than a tile.
The quarter-circle Truchet tile most people know came much later, from Cyril Stanley Smith in 1987. The tide control swaps the tones across a diagonal, the way the posters it resembles change colour halfway down the sheet.
Behind the mathematics
Dominique Douatfl. 1722
Designs by rule from a motif, 1722
Carmelite friar who took Truchet's divided square and showed that a few tiles, arranged by rule rather than by eye, generate an unlimited catalogue of designs.