In information visualization and graphic design, Truchet tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed within a square tiling of the plane, they can form varied patterns, and the orientation of each tile can be used to visualize information associated with the tile's position within the tiling.
The tiles originally studied by Truchet use a pattern in which each tile is split into two triangles of contrasting colors. Each such tile has four possible orientations.
Some examples of surface filling made tiling such a pattern.
With a scheme:
With random placement:
A second common form of the Truchet tiles, due to Smith (1987), decorates each tile with two quarter-circles connecting the midpoints of adjacent sides. Each such tile has two possible orientations.
We have such a tiling:
Fournier resumed Truchet's work and proposed alternative patterns:
With Fournier pattern we obtain:
As a curiosity, a simple maze can be generated by tiles in the form of a white square with a black diagonal. As with the quarter-circle tiles, each such tile has two orientations.
|Wikimedia Commons has media related to Truchet tiles.|
- Browne, Cameron (2008), "Truchet curves and surfaces", Computers & Graphics 32 (2): 268–281, doi:10.1016/j.cag.2007.10.001.
- Smith, Cyril Stanley (1987), "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy", Leonardo 20 (4): 373–385, doi:10.2307/1578535. With a translation of Truchet's text by Pauline Boucher.
- Weisstein, Eric W., "Truchet Tiling", MathWorld.
- Truchet in 2D and 3D: http://local.wasp.uwa.edu.au/~pbourke/texture_colour/periodic/