In his 1704 paper, Mémoire sur les combinaisons, Sébastien Truchet studied a curious tile that, when rotated to different orientations, could form countless aesthetic patterns.^[1]

This project contains the 30 patterns engraved in Truchet's memoir, though he notes (translated from French) that "We found too great a number to report them all."^[2] I've added some more patterns, mainly those that differ from Truchet's scheme by patterning each quadrant differently instead of uniformly.

This project animates transitions between various patterns, allowing you to adjust the switch style and switch frequency to determine what order and how often the tiles get switched. You can autoplay to automatically switch between random patterns (using the adjacent slider to adjust the delay between pattern switching). You can optionally turn on colors to highlight the new orientation of tile.

The size of the plane can be adjusted by the number of rows and columns. By pressing on or hovering over (depending on the manual switch on setting) tiles you can manually switch them, which automatically updates your URL. In the interest of performance, this page transcribes and loads a maximum of 20 rows and 20 columns in sharable URLs.

For more information, Cyril Stanley Smith's 1987 paper The Tiling Patterns of Sebastian Truchet and the Topology of Structural Hierarchy provides a translation of Truchet's original text and a deeper look at Truchet tiling.^[2] Additionally, Dominique Douat's 1722 book provides an extensive exploration of generating Truchet tiling.^[3]

Project inspired by wavegrower's animation of Smith Truchet tiles.