3D Printer Templates for Wang Tiles

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This Demonstration shows Wang tiles for Turing machines. The Turing machines use two symbols and , with states , , …, . Rectangles and disks are used for the symbols. The states of the machine are represented by regular -gons. The operation of the machine is represented by tiles, such as the following:


The first is called the alphabet tile, the next two are merging tiles and the last two represent action tiles: and .


Contributed by: Izidor Hafner (February 2020)
Open content licensed under CC BY-NC-SA



This modification of Wang tiles was introduced by Robinson [1]. The photo shows a tiling that corresponds to a Turing machine that starts with a tape of rectangles and the head moves to the right.


[1] R. M. Robinson, "Undecidability and Nonperiodicity for Tilings of the Plane," Inventiones Mathematicae, 12(3), 1971 pp. 177–209. doi:10.1007/BF01418780.

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