# Truchet tiles

In information visualization and graphic design, Truchet tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed within a square tiling of the plane, they can form varied patterns, and the orientation of each tile can be used to visualize information associated with the tile's position within the tiling.[1]

Truchet tiles were first described in a 1704 memoir by Sébastien Truchet entitled "Memoir sur les Combinaisons", and were popularized in 1987 by Cyril Stanley Smith.[1][2]

## Variations

### Contrasting triangles

The tiles originally studied by Truchet use a pattern in which each tile is split into two triangles of contrasting colors. Each such tile has four possible orientations.

Some examples of surface filling made tiling such a pattern.

With a scheme:

With random placement:

### Quarter-circles

A second common form of the Truchet tiles, due to Smith (1987), decorates each tile with two quarter-circles connecting the midpoints of adjacent sides. Each such tile has two possible orientations.

The Truchet tile
Inverse of the Truchet tile, created by any 90° rotation or orthogonal flip

We have such a tiling:

This type of tile has also been used in abstract strategy games Trax and the Black Path Game, prior to Smith's work.[1]

### Fournier pattern

Fournier resumed Truchet's work and proposed alternative patterns:

With Fournier pattern we obtain:

### Diagonal

As a curiosity, a simple maze can be generated by tiles in the form of a white square with a black diagonal. As with the quarter-circle tiles, each such tile has two orientations.