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Wang tiles are square unit tiles with colored edges. A finite set of Wang tiles is a valid tile set if the collection tiles the plane (using an unlimited number of copies of each tile), the only requirements being that adjacent tiles must have common edges with matching colors and each tile can be put in place only by translation. In 1995 Kari and Culik gave examples of tile sets with 14 and 13 Wang tiles respectively, which only tiled the plane aperiodically. Their tile sets were constructed using a piecewise multiplicative function of an interval. The fact the sets tile only aperiodically is derived from properties of the function.

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