Truchet Blocks

Tasks

	Make your own blobby designs. Use the blocks to make a square or a cube.
	Can you make a 2×2 design that is just one connected blue blob and one connected white blob?
	How many different blocks are there?

Maths

The faces of the blocks are called Truchet tiles. They are made of two quarter-circles in opposite corners of a square. There are two types of Truchet tile:

Together they make fun blobby patterns like this:

Which can then be coloured in like this:

Different combinations can make very different designs.

We used the Truchet tiles to make our blocks. Two blocks can look different but, when you rotate the block, they are actually the same. So how many different blocks are there?

Each face of our blocks either have a blue stripe down the middle, or a white stripe down the middle. If you consider all the blocks that have 0 blues stripes, 1 blue stripe, 2 blue stripes, 3 blue stripes, 4 blue stripes, 5 blue stripes and 6 blue stripes you get this set of twelve blocks:

History

Jean Truchet was a French priest in the late 1600s. Truchet was interested in decorative ceramic tilings, and designed a set of tiles, divided diagonally, with contrasting colours:

Truchet then investigated how many ways there were to combine the tiles, noting that some of the possibilities were the same after rotation. And in fact there are only ten different ways to combine two tiles side-by-side.

This set of tiles could then be used to make interesting designs.

Truchet tiles using quarter-circles were popularised in 1987 by Cyril Smith, a historian of science.

People

	Sébastien Truchet 1657 – 1729 Sebastien Truchet was a French priest who was interested in mathematics, hydraulics and typography. Truchet used his mathematical skills to design canals, sundials, and typefaces (fonts) used in printing. Inspired by designs he had seen on the canal, Truchet designed a set of ceramic tiles that could be used to make interesting geometric designs.
Stanislav Smirnov 1970 – Present Smirnov is a Russian mathematician currently working at the University of Geneva. In 2010 Smirnov won the Fields medal (a maths prize as important as a Nobel prize) for his work on percolation theory which describes how networks link together, like Truchet tilings.

Applications

Truchet’s original idea was to use his set of tiles to create interesting ceramic designs.

Randomised tilings can be used to give surfaces texture in computer graphics, which look natural and non-repeating.

Truchet tilings are an example of percolation theory, which is the study of how networks link together. This has applications in the study of porous materials such as sandstone or Swiss cheese because slice of these materials will have connected regions similar to a truchet tiling.