# 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]}

## Contents

## Variations[edit]

### Contrasting triangles[edit]

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:

### Quarter-circles[edit]

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:

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[edit]

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]}

## See also[edit]

Wikimedia Commons has media related to .Truchet tiles |

## References[edit]

- ^
^{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[edit]

- 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)