Truchet tiles
Truchet Tiles Interactive App
Math exercise: what's the probability of no circle?
Truchet Tiles
The idea can easily be extended to 3D.
Combinatorial Technique to Generate Decorative Patterns
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 overall 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:
