Nonperiodic Substitution Tiling of the Plane

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The substitution rule specified in this Demonstration enables filling and then inflation of a tile into four copies of itself. Iterating these rules forms larger and larger "supertiles" and ultimately defines substitution tilings, which are divisions of the plane into infinite hierarchies of supertiles. The inflation factor is four, and geometric transformations such as rotations and reflections are applied to define the supertiles.

Contributed by: Wolfgang Hitzl (December 2017)
Open content licensed under CC BY-NC-SA


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References

[1] I. Stewart, "Ungewöhnliche Kachelungen," Spektrum der Wissenschaft 11, 2001 p. 114. www.spektrum.de/magazin/ungewoehnliche-kachelungen/828148.

[2] Wikipedia. "Substitution Tiling." (Dec 1, 2017) en.wikipedia.org/wiki/Substitution_tiling.

[3] Tilings Encyclopedia. "Substitution." (Dec 1, 2017) tilings.math.uni-bielefeld.de/glossary/substitution.



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