Läuchli

In 1975 an aperiodic set of 40 tiles was discovered by Hans Läuchli. At the time this was the smallest set of aperiodic tiles known. The tiles were Wang tiles – square tiles that have edge values that must match. In Läuchli’s tile set, each tile had lines that, if they met an edge of a tile, had to be continued in the adjacent tile. Some tile edges were also thicker/darker than others and these also had to match. This is illustrated left below, which is based on Läuchli’s representation of his tiles. The rendering on the right is my alternative rendering of the same tile arrangement, although I have used artist’s licence to not show the tile edges at all.