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March 14th 2010

Truchet patterns

I haven't been posting much lately. Fortunately, it's time, not inspiration which is missing.

I've often mentionned Truchet patterns previously, referring each time to the Wikipedia article. It's probably worth making a post explaining the basics and displaying a few examples.

The idea behind Truchet pattern is fairly simple. Start from a regular tiling of the plane (most often a square tiling), as well as a set of tile decorations. Then apply to each tile 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 (see the Wikipedia article). It is more interesting to devise the decorations so that they merge smoothly at the edges of the tiles, hiding the underlying tiling.

My works based on Truchet patterns can be found here. Let us describe now a few examples.

Truchet tile decoration Truchet tile decoration

Two decorations of square tiles...

A Truchet pattern

...and the Truchet pattern constructed by applying them randomly to a square tiling. Two elementary squares carrying the two types of decorations are highlighted in red.

A Truchet pattern

Here, two different sets of decorations are used on two subsets of the square tiling. Those correspond to the tiles colored black and white on a checker.

A Truchet pattern

In this case, the decorations are similar as in the first example, except that the circle arcs are replaced by straight diagonal lines.

A Truchet pattern

In this case, there are a larger number of decorations. Like in the first example, each decoration is composed of non-intersecting "strings" drawn on the squares. While in the first example, one string was crossing each edge of the squares, here two strings do.

A Truchet pattern

This Truchet pattern is constructed from only two of the decorations used in the previous example.

A Truchet pattern

Here, a hexagonal tiling has been used, instead of a square one.

A Truchet pattern

A variation also based on an hexagonal tiling.

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