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Celtic Knots, Truchet tiles, Combinatorial Patterns
Xah Lee, 2010-06-25
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 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.