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Penrose tilings as model sets

Penrose tilings as model sets Abstract The Baake construction, based on generating a set of vertices of Penrose tilings as a model set, is refined. An algorithm and a corresponding computer program for constructing an uncountable set of locally indistinguishable Penrose tilings are developed proceeding from this refined construction. Based on an analysis of the parameters of tiling vertices, 62 versions of rhomb combinations at the tiling center are determined. The combinatorial structure of Penrose tiling worms is established. A concept of flip transformations of tilings is introduced that makes it possible to construct Penrose tilings that cannot be implemented in the Baake construction. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Crystallography Reports Springer Journals

Penrose tilings as model sets

Crystallography Reports , Volume 60 (6): 8 – Nov 1, 2015

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References (28)

Publisher
Springer Journals
Copyright
2015 Pleiades Publishing, Inc.
ISSN
1063-7745
eISSN
1562-689X
DOI
10.1134/s1063774515060322
Publisher site
See Article on Publisher Site

Abstract

Abstract The Baake construction, based on generating a set of vertices of Penrose tilings as a model set, is refined. An algorithm and a corresponding computer program for constructing an uncountable set of locally indistinguishable Penrose tilings are developed proceeding from this refined construction. Based on an analysis of the parameters of tiling vertices, 62 versions of rhomb combinations at the tiling center are determined. The combinatorial structure of Penrose tiling worms is established. A concept of flip transformations of tilings is introduced that makes it possible to construct Penrose tilings that cannot be implemented in the Baake construction.

Journal

Crystallography ReportsSpringer Journals

Published: Nov 1, 2015

Keywords: Crystallography and Scattering Methods

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