Symmetries and Antisymmetries of Truchet Rosettes

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.

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.