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<p>Die Seite wurde neu angelegt: „ == Reference == Edmund Harriss: <a href="/index.php?title=Images_of_the_Ammann-Beenker_Tiling" title="Images of the Ammann-Beenker Tiling">Images of the Ammann-Beenker Tiling</a>. In: <a href="/index.php?title=Bridges_2007" title="Bridges 2007">Bridges 2007</a>. Pages 377–378 == DOI == == Abstract == The Ammann-Beenker …“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Edmund Harriss: [[Images of the Ammann-Beenker Tiling]]. In: [[Bridges 2007]]. Pages 377–378 <br /> == DOI ==<br /> <br /> == Abstract ==<br /> The Ammann-Beenker tiling is the eight-fold sibling of the more famous, five-fold Penrose rhomb<br /> tiling. It was discovered independently by R. Ammann [AGS92] and F. Beenker [Bee82]. It shares many<br /> properties with the Penrose tiling. In particular it shares two particular constructions. The first by a<br /> substitution rule1 , and the second as a slice of a higher dimensional lattice. Also it shares the important<br /> property with the Penrose that it is a strikingly beautiful tiling.<br /> <br /> R. Ammann’s discovery of the tiling was at the same<br /> time as Penrose’s. In fact he sent in several examples in<br /> response to Martin Gardener’s Scientific America arti-<br /> cle that announced the Penrose tiling [Gar77]. Though<br /> it was only later that something was published more for-<br /> mally, as Ammann was very detached from the math-<br /> ematical community[Sen04]. Like Penrose (and nearly<br /> all the early aperiodic tilings) he used a substitution rule<br /> to construct the tiling. ...<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [AGS92] R Ammann, B Gr ̈unbaum, and G C Shephard, Aperiodic tiles, Discrete Comput. Geom. 8<br /> (1992), no. 1, 1–25. MR 93g:52015<br /> <br /> [Bee82] F P M Beenker, Algebraic theory of non-periodic tilings of the plane by two simple building<br /> blocks: a square and a rhombus, TH-Report 82-WSK04, Eindhoven University of Technology,<br /> 1982.<br /> <br /> [dB81] N G de Bruijn, Algebraic theory of Penrose’s nonperiodic tilings of the plane. I, II, Nederl.<br /> Akad. Wetensch. Indag. Math. 43 (1981), no. 1, 39–52, 53–66. MR 82e:05055<br /> <br /> [Gar77] M Gardner, Extraordinary nonperiodic tiling that enriches the theory of tiles, Sci. Am.<br /> November (1977), 110–119.<br /> <br /> [Har03] E O Harriss, On canonical substitution tilings, Ph.D. thesis, Imperial College London, 2003.<br /> <br /> [Sen04] Marjorie Senechal, The mysterious Mr. Ammann, Math. Intelligencer 26 (2004), no. 4, 10–21.<br /> MR MR2104463 (2005j:52026)<br /> <br /> [Soc89] J E S Socolar, Simple octagonal and dodecagonal quasicrystals, Phys. Rev. B (3) 39 (1989),<br /> no. 15, 519–551. MR 90h:52019<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2007/bridges2007-377.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2007/bridges2007-377.html</div>

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