Truchet tiles

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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.[1]

Truchet tiles were first described in a 1704 memoir by Sébastien Truchet entitled "Memoir sur les Combinaisons", and were popularized in 1987 by Cyril Stanley Smith.[1][2]

Variations[edit]

Contrasting triangles[edit]

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.

Truchet base tiles bordered.png

Some examples of surface filling made tiling such a pattern.

With a scheme:

Truchet ordered tiling.svg

With random placement:

Truchet base tiling.svg

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.

Truchet tile
The Truchet tile
Truchet tile inverse
Inverse of the Truchet tile, created by any 90° rotation or orthogonal flip

We have such a tiling:

Truchet tiling.svg

This type of tile has also been used in abstract strategy games Trax and the Black Path Game, prior to Smith's work.[1]

Fournier pattern[edit]

Fournier resumed Truchet's work and proposed alternative patterns:

Fournier tile.png

With Fournier pattern we obtain:

Fournier tiling.svg

Diagonal[edit]

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.

Truchet labyrinth.png

See also[edit]

References[edit]

  1. ^ a b c Browne, Cameron (2008), "Truchet curves and surfaces", Computers & Graphics 32 (2): 268–281, doi:10.1016/j.cag.2007.10.001 .
  2. ^ 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.

External links[edit]