# Celtic Knots, Truchet tiles, Combinatorial Patterns

Xah Lee, 2010-06-25

A image made by Henry Segerman.

Basically, this method is just a combination of square tiles. Each tile has a pattern. When 2 tiles are placed together, the pattern on them connect at the edges. When a bunch of these tiles are placed together, each tile may have different pattern or orientation, they form various knots or paths. If each tile's pattern and orientation is choosen carefully, a symmetric over all design can be created.

This way of creating patterns is known as Truchet tiles.

It can be done with equilateral triangles too, or, any tiling of n polygonal prototiles. Just make sure that the patterns on each tile is such that their edge can connect smoothly.

For several tiles by the truchet tile method, see:

Truchet tiles. Floor by Colin Fizgig, tube by Sleeves Rhode. These are created in Second Life.

The idea can easily be extended to 3D.

3D version by Sleeves.

A Hyperbolic Paraboloid, on a background several tilings by the Truchet method. For info about the metal surface, see: Math in Second Life (page 2)