Truchet tiles
In information visualization and graphic design, Truchet tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed in 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.[1]
Truchet tiles were first described in a 1704 memoir by Sébastien Truchet entitled "Mémoire sur les combinaisons", and were popularized in 1987 by Cyril Stanley Smith.[1][2]
Variations[]
Contrasting triangles[]
The tile originally studied by Truchet is split along the diagonal into two triangles of contrasting colors. The tile has four possible orientations.
![Truchet base tiles bordered.png](http://upload.wikimedia.org/wikipedia/commons/d/d9/Truchet_base_tiles_bordered.png)
Some examples of surface filling made tiling such a pattern.
With a scheme:
![Truchet ordered tiling.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Truchet_ordered_tiling.svg/562px-Truchet_ordered_tiling.svg.png)
With random placement:
![Truchet base tiling.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Truchet_base_tiling.svg/250px-Truchet_base_tiling.svg.png)
Quarter-circles[]
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.
![Truchet tile](http://upload.wikimedia.org/wikipedia/commons/thumb/1/12/Truchet_tile.svg/120px-Truchet_tile.svg.png)
![Truchet tile inverse](http://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Truchet_tile_inverse.svg/120px-Truchet_tile_inverse.svg.png)
We have such a tiling:
![Truchet tiling.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/0/00/Truchet_tiling.svg/250px-Truchet_tiling.svg.png)
This type of tile has also been used in abstract strategy games Trax and the Black Path Game, prior to Smith's work.[1]
Diagonal[]
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.[3]
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$(205.5+RND(1)); : GOTO 10
- to be "a concrete poem, a found poem".[3]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Truchet_labyrinth.png/250px-Truchet_labyrinth.png)
See also[]
![]() |
Wikimedia Commons has media related to Truchet tiles. |
- Girih tiles
- Wallpaper group
- Wang tiles
References[]
- ^ a b c Browne, Cameron (2008), "Truchet curves and surfaces", Computers & Graphics, 32 (2): 268–281, doi:10.1016/j.cag.2007.10.001.
- ^ Smith, Cyril Stanley (1987), "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy", Leonardo, 20 (4): 373–385, doi:10.2307/1578535. With a translation of Truchet's text by Pauline Boucher.
- ^ a b Montfort, Nick (2012). 10 PRINT CHR$(205.5+RND(1)); : GOTO 10. MIT Press.
External links[]
- Weisstein, Eric W. "Truchet Tiling". MathWorld.
- Truchet in 2D and 3D: https://web.archive.org/web/20120820024223/http://local.wasp.uwa.edu.au/~pbourke/texture_colour/periodic/
- Javascript animation: http://perso.orange.fr/jean-paul.davalan/divers/truchet/truc.html (unknown page, 19.05.06)
- Tessellation
- Patterns