To begin at a beginning.
The figure below shows just four interlocking supertiles of a typical member of the Chinese Lattice Labyrinth family, member (9,6) a case with separation parameters (a,b) where a and b share a common factor, 3 in this case. Such common-factor cases require a little more finesse in the construction process but tend to be attractive.
To embolden the effect of the illustration, I’ve hidden the boundaries of the 117 square tiles that make up each supertile. You can see how this pattern could be extended by repetition in all directions until the infinite plane bumps up against the edge of the Universe, or comes round to meet itself again.
And shall be ever further. (A Googlewhack) – and while we’re contemplating infinity, suppose we wind up the order a little, to Chinese Labyrinth (27,18), also a member of the (3a,2a) common-factor sub-family. In this case it’s the highest common factor, 9, rather than 3, that determines the construction.
Notice the similarity. For an even higher-order member of this sub-family, see the Chinese Labyrinth (39,26) post.