Truchet patterns are generated from a tiling of the plane (a square tiling for the images below), as well as a set of tile decorations. Each tile is then applied a random decoration. Because of the random choice, the underlying regularity of the tiling is broken, what yields interesting patterns.

Truchet's original decorations consist in dividing the square into two triangles along a diagonal and paint them with different colors.

But it is more interesting to devise the decorations so that they merge smoothly at the edges of the tiles, hiding the underlying tiling. For instance, imagine using either of the first two decorations below on the black squares of a checkerboard, and either of the last two decorations on the white ones.

Choosing them randomly yields the following kind of patterns, after a rotation of 45°.

Interesting emergent pattern arise when the decorations are not chosen at random, but rather according to an underlying pattern, for instance here another square tiling, possibly scaled and rotated.

The pattern can also be varied by changing the decoration of the tiles, for instance here to make the black lines thinner

Dall-e's interpretation of Truchet patterns