Hyperbolic Truchet Tilings

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Douglas Dunham: Hyperbolic Truchet Tilings. In: Bridges 2011. Pages 311–318



About 300 years ago S ́ebastien Truchet systematically studied patterns that could be formed from square tiles that were divided by a diagonal into a white triangle and a black triangle. Other pattern creators have been inspired by him to make Truchet-like tilings composed of circular arcs and other motifs. These tilings are all based on Euclidean tessellations, usually the tiling by squares. In this paper we extend the concept of a Truchet tiling to the hyperbolic plane and show some sample patterns.

Extended Abstract


Used References

[1] Cameron Browne, Duotone Truchet-like tilings, Journal of Mathematics and the Arts, 2: pp. 189–196, 2008.

[2] The Wikipedia page on Pierre Simon Fournier: http://en.wikipedia.org/wiki/Pierre_Simon_Fournier

[3] R.A. Lord and S. Ranganathan, Truchet tilings and their generalisations, Resonance, Vol. 11, No. 6, pp. 42–50, 2006.

[4] David Reimann, Text from Truchet Tiles, Bridges 2009 Conference Proceedings, pp. 325–326, 2009.

[5] David Reimann, Patterns from Archimedean Tilings Using Generalized Truchet Tiles Decorated with Simple B ́ezier Curves, Bridges 2010 Conference Proceedings, pp. 427–430, 2010.

[6] Sleeves Rhode patterns at: http://xahlee.org/math/Truchet_tiles.html

[7] Cyril Stanley Smith, The tiling patterns of Sebastien Truchet and the topology of structural hierarchy, Leonardo, 20(4): 373–385, 1987.

[8] S ́ebastien Truchet, M ́emoire sur les combinaisons, Memoires de l’Academie Royale des Sciences, pp. 363–372, 1704.

[9] S. Truchet, Wikipedia page: http://en.wikipedia.org/wiki/Sebastien_Truchet


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