Images of the Ammann-Beenker Tiling
Inhaltsverzeichnis
Reference
Edmund Harriss: Images of the Ammann-Beenker Tiling. In: Bridges 2007. Pages 377–378
DOI
Abstract
The Ammann-Beenker tiling is the eight-fold sibling of the more famous, five-fold Penrose rhomb tiling. It was discovered independently by R. Ammann [AGS92] and F. Beenker [Bee82]. It shares many properties with the Penrose tiling. In particular it shares two particular constructions. The first by a substitution rule1 , and the second as a slice of a higher dimensional lattice. Also it shares the important property with the Penrose that it is a strikingly beautiful tiling.
R. Ammann’s discovery of the tiling was at the same time as Penrose’s. In fact he sent in several examples in response to Martin Gardener’s Scientific America arti- cle that announced the Penrose tiling [Gar77]. Though it was only later that something was published more for- mally, as Ammann was very detached from the math- ematical community[Sen04]. Like Penrose (and nearly all the early aperiodic tilings) he used a substitution rule to construct the tiling. ...
Extended Abstract
Bibtex
Used References
[AGS92] R Ammann, B Gr ̈unbaum, and G C Shephard, Aperiodic tiles, Discrete Comput. Geom. 8 (1992), no. 1, 1–25. MR 93g:52015
[Bee82] F P M Beenker, Algebraic theory of non-periodic tilings of the plane by two simple building blocks: a square and a rhombus, TH-Report 82-WSK04, Eindhoven University of Technology, 1982.
[dB81] N G de Bruijn, Algebraic theory of Penrose’s nonperiodic tilings of the plane. I, II, Nederl. Akad. Wetensch. Indag. Math. 43 (1981), no. 1, 39–52, 53–66. MR 82e:05055
[Gar77] M Gardner, Extraordinary nonperiodic tiling that enriches the theory of tiles, Sci. Am. November (1977), 110–119.
[Har03] E O Harriss, On canonical substitution tilings, Ph.D. thesis, Imperial College London, 2003.
[Sen04] Marjorie Senechal, The mysterious Mr. Ammann, Math. Intelligencer 26 (2004), no. 4, 10–21. MR MR2104463 (2005j:52026)
[Soc89] J E S Socolar, Simple octagonal and dodecagonal quasicrystals, Phys. Rev. B (3) 39 (1989), no. 15, 519–551. MR 90h:52019
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Full Text
http://archive.bridgesmathart.org/2007/bridges2007-377.pdf
