Celtic Knots, Truchet tiles, Combinatorial Patterns

By Xah Lee. Date:
knot puzzle
A Celtic knot design by Henry Segerman.

This is made by using a “Celtic Knot font” (from clanbadge.com).

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 chosen carefully, a over all symmetric design can be created, and can be very striking.

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 pattern designs by the truchet tile method, see:

sq arc503Tile-p sq squarly weave-p t hexagon link-p sq lotus vine weaving-p
Truchet tiles
Truchet tiles. Floor by Colin Fizgig, tube by Sleeves Rhode. These are created in Second Life.

The idea can easily be extended to 3D.

Truchet tiles 3d
3D version by Sleeves.
hyperbolic paraboloid
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