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 tile originally studied by Truchet is split along the diagonal into two triangles of contrasting colors. The 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:
A labyrinth 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. The connectivity of the resulting labyrinth can be analyzed mathematically using percolation theory as bond percolation at the critical point of a diagonally-oriented grid. Nick Montfort considers the single line of Commodore 64 BASIC required to generate such patterns -
10 PRINT CHR$(205.5+RND(1)); : GOTO 10 - to be "a concrete poem, a found poem".
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- Browne, Cameron (2008), "Truchet curves and surfaces", Computers & Graphics, 32 (2): 268–281, doi:10.1016/j.cag.2007.10.001.
- Smith, Cyril Stanley (1987), "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy", Leonardo, 20 (4): 373–385, doi:10.2307/1578535. With a translation of Truchet's text by Pauline Boucher.
- Montfort, Nick (2012). 10 PRINT CHR$(205.5+RND(1)); : GOTO 10. MIT Press.
- Truchet in 2D and 3D: http://local.wasp.uwa.edu.au/~pbourke/texture_colour/periodic/