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.
![](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:
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Truchet_ordered_tiling.svg/562px-Truchet_ordered_tiling.svg.png)
With random placement:
![](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:
![](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$(205.5+RND(1)); : GOTO 10
- to be "a concrete poem, a found poem".[3]
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Truchet_labyrinth.png/250px-Truchet_labyrinth.png)
See also
![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
- Girih tiles
- Wallpaper group
- Wang tiles
References
- ^ a b c Browne, Cameron (2008), "Truchet curves and surfaces", Computers & Graphics, 32 (2): 268–281, doi:10.1016/j.cag.2007.10.001.
- ^ Smith, Cyril Stanley (1987), "The tiling patterns of Sebastian Truchet and the topology of structural hierarchy", Leonardo, 20 (4): 373–385, doi:10.2307/1578535, JSTOR 1578535. With a translation of Truchet's text by Pauline Boucher.
- ^ a b Montfort, Nick (2012). 10 PRINT CHR$(205.5+RND(1)); : GOTO 10. MIT Press.
External links
- Weisstein, Eric W. "Truchet Tiling". MathWorld.
- Online Truchet Pattern Generator: https://truchetpatterns.netlify.app/
- Ibáñez, Raúl, "The Truchet Tiles and the Diamond Puzzle"
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