Linear mappings as self-similarities of mathematical models of quasicrystals

In this paper an overview of the so-called cut-and-project method is presented together with new results on the construction of a cut-and-project set with a given linear diagonalizable self-similarity A. Such a construction is illustrated on a two-dimensional mathematical quasicrystal related to the...

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Published inJournal of physics. Conference series Vol. 1194; no. 1; pp. 12005 - 12013
Main Authors Ambrož, Petr, Masáková, Zuzana, Mazáč, Jan
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.04.2019
Subjects
Mathematical analysis
Mathematical models
Quasicrystals
Self-similarity
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Summary:In this paper an overview of the so-called cut-and-project method is presented together with new results on the construction of a cut-and-project set with a given linear diagonalizable self-similarity A. Such a construction is illustrated on a two-dimensional mathematical quasicrystal related to the Pisot number 1 + 2 cos 2 π 7 . This model is described in detail and the associated Voronoi tilling is discussed. Moreover, it is shown that there exists a connection between the planar quasicrystal and higher-dimensional quasicrystal with 7-fold symmetry.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1194/1/012005