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Truchet Tiling


TruchetTriangularTiles

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875).

TruchetTriangularTiling

Truchet's tiles produce beautiful patterns when laid out on a grid, as illustrated by the 20×20 arrangement of random tiles illustrated above.

TruchetTile

A modification of Truchet's tiles leads to a single tile consisting of two circular arcs of radius equal to half the tile edge length centered at opposed corners (Pickover 1989). There are two possible orientations of this tile, and tiling the plane using tiles with random orientations gives visually interesting patterns. In fact, these tiles have been used in the construction of various games, including the "black path game" and "meander" (Berlekamp et al. 1982, pp. 682-684).

TruchetPattern

The illustration above shows a 20×20 Truchet tiling. For random orientations, the fraction of closed circles is approximately 0.054 and the fraction of dumbbell shapes is approximately 0.0125 (Pickover 1989).


See also

b-Cluster, s-Cluster

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References

Artlandia, Inc. "Graphica 2 and Beyond: Creating Artistic Images with Artlandia." http://library.wolfram.com/infocenter/MathSource/156/.Berlekamp, E. R.; Conway, J. H.; and Guy, R. K. Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, 1982.Dewdney, A. K. The Magic Machine: A Handbook of Computer Sorcery. New York: Freeman, 1990.Gale, D.; Propp, J.; Sutherland, S.; and Troubetzkoy, S. "Further Travels with My Ant." Math. Intell. 17, No. 3, 48-56, 1995.Pickover, C. Computers, Pattern, Chaos and Beauty. New York: St. Martin's Press, 1991.Pickover, C. A. "Picturing Randomness with Truchet Tiles." J. Recr. Math. 21, 256-259, 1989.Smith, C. S. "The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy." Leonardo 20, 373-385, 1987.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 875, 2002.

Referenced on Wolfram|Alpha

Truchet Tiling

Cite this as:

Weisstein, Eric W. "Truchet Tiling." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TruchetTiling.html

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