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2014 | 126 | 2 | 493-496
Article title

Tiling Vertices and the Spacing Distribution of Their Radial Projection

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EN
Abstracts
EN
The Fourier-based diffraction approach is an established method to extract order and symmetry properties from a given point set. We want to investigate a different method for planar sets which works in direct space and relies on reduction of the point set information to its angular component relative to a chosen reference frame. The object of interest is the distribution of the spacings of these angular components, which can for instance be encoded as a density function on ℝ_+. In fact, this radial projection method is not entirely new, and the most natural choice of a point set, the integer lattice ℤ², is already well understood. We focus on the radial projection of aperiodic point sets and study the relation between the resulting distribution and properties of the underlying tiling, like symmetry, order and the algebraic type of the inflation multiplier.
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EN
Publisher

Year
Volume
126
Issue
2
Pages
493-496
Physical description
Dates
published
2014-08
Contributors
author
  • Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
References
  • [1] M. Baake, U. Grimm, Aperiodic Order. Vol. I, A Mathematical Invitation, Cambridge University Press, Cambridge 2013
  • [2] F.P. Boca, C. Cobeli, A. Zaharescu,Commun. Math. Phys. 213, 433 (2000), doi: 10.1007/s002200000250
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv126n217kz
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