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Symmetries and Antisymmetries of Truchet Rosettes

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In the beginning of the eighteenth century, the French priest Sébastien Truchet explored patterns made with a simple motif: a square divided by one of its diagonals into two colored triangles, now known as a Truchet tile.

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Use this Demonstration to create a rosette made of Truchet tiles and explore its symmetry and antisymmetry properties:

1. Choose the dimensions of the rosette by setting the "rows" and "columns" buttons.

2. Create your design by clicking the tiles of the original rosette.

3. Apply different transformations to observe symmetries or antisymmetries of the rosette.

You can choose any of the square symmetries (rotations of multiples of a right angle or reflections over four possible lines). In addition, you can select the "reverse colors" button and couple it with one of the isometries to produce antisymmetries. By antisymmetry, we mean reversal of black and white.

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Contributed by: Andreia Hall, António Pereira, João Nunes and Paolo Vettori (June 13)
Open content licensed under CC BY-NC-SA

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References

[1] A. Hall, P. Almeida and R. Teixeira, "Exploring Symmetry in Rosettes of Truchet Tiles," Journal of Mathematics and the Arts, 13(4), 2019 pp. 308–335. doi:10.1080/17513472.2019.1581963.

[2] L. Radovic and S. Jablan, "Antisymmetry and Modularity in Ornamental Art," Bridges: Mathematical Connections in Art, Music, and Science (R. Sarhangi and S. Jablan, eds.), Winfield, KS: Bridges Conference, 2001 pp. 55–66. archive.bridgesmathart.org/2001/bridges2001-55.html.

[3] C. S. Smith and P. Boucher, "The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy," Leonardo, 20(4), 1987 pp. 373–385. doi:10.2307/1578535.

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