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A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3] The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are ...
Berger later reduced his set to 104, and Hans Läuchli subsequently found an aperiodic set requiring only 40 Wang tiles. [9] The set of 13 tiles given in the illustration on the right is an aperiodic set published by Karel Culik, II, in 1996. However, a smaller aperiodic set, of six non-Wang tiles, was discovered by Raphael M. Robinson in 1971 ...
The tiles in the square tiling have only one shape, and it is common for other tilings to have only a finite number of shapes. These shapes are called prototiles, and a set of prototiles is said to admit a tiling or tile the plane if there is a tiling of the plane using only these shapes.
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Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, is a class of formal systems. They are modeled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.