Trushche tiles are square tiles with a pattern that does not have rotational symmetry . Located in the form of a square mosaic on a plane, they can form various patterns [1] .
First met in the writings of the Dominican monk , entitled "Memoir sur les Combinaisons" (from Fr. - "Memoirs of combinations") and dating from 1704 ; were popularized and received a modern name in 1987 in the works of Cyril Stanley Smith [1] [2] . They are widely used in the fields of , graphic design .
Content
Variations
Contrast Triangles
The tiles that Trushche originally studied had a pattern in the form of two triangles with contrasting colors. Each such tile has four possible orientations.
Some examples of filling a plane with such tiles.
According to the scheme:
Random orientation selection:
Quarter-circle
According to Smith [3] , the second common type of tiles Trushé has a pattern on each tile in the form of two quarters of a circle connecting the middle of adjacent sides. Each such tile has two variants of orientation.
An example of such a mosaic:
This type of tile was used in the abstract strategic games " Trucks " and even before Smith [1] .
Diagonal
As a curiosity, a simple maze can be obtained from a tile in the form of a white square with a black diagonal. As in the case of a tile with two quarters of circles, each such tile has two orientations.
See also
- Mosaics "girih"
- Wallpaper group
Notes
- ↑ 1 2 3 Browne, 2008 , p. 268–281.
- ↑ Smith, 1987 , p. 373-385.
- ↑ Smith, 1987 .
Literature
- Cameron Browne. Truchet curves and surfaces // Computers & Graphics. - 2008. - V. 32 , no. 2 - DOI : 10.1016 / j.cag.2007.10.001 .
- Cyril Stanley Smith. The tiling patterns of the Sebastian Truchet and the topology of the structural hierarchy // Leonardo . - 1987. - V. 20 , no. 4 - DOI : 10.2307 / 1578535 .
Links
- Weisstein, Eric W. Truchet Tiling (English) on the Wolfram MathWorld website.
- 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