A small aperiodic set of Wang tiles
A Wang tile is a unit square tile with colored edges. Consider tilings of the Euclidean plane by arbitrarily many copies from a given finite tile set \(T\) of Wang tiles translated to integer lattice points and such that contiguous edges have the same color. Such a tiling, determined by a function \(f:Z^2\to T\), is periodic if there exists \((a,b)\in Z^2\backslash\{(0,0)\}\) such that \(f(x,y)= f(x+a,y+b)\) for every \((x,y)\in Z^2\). A tile set \(T\) is called aperiodic if there exists a tiling, but there does not exist any periodic tiling. In 1966 \textit{R. Berger} [Mem. Am. Math. Soc. 66 (1966; Zbl 0199.30802)] constructed an aperiodic tile set consisting of over 20,000 Wang tiles. The number has since been reduced, including a set consisting of 16 Wang tiles due to R. Amman. In the paper under review, the number is further reduced to 14 Wang tiles.
scientific article; zbMATH DE number 955162