About Substitution Tilings with Statistical Circular Symmetry
Dirk Frettl\"oh
TL;DR
This paper investigates the distribution of tile orientations in primitive substitution tilings, revealing results for both finite and infinite orientation sets, and explores implications for diffraction spectra and dynamical systems.
Contribution
It presents new results on the equidistribution of tile orientations in substitution tilings, extending understanding to both finite and infinite cases.
Findings
Equidistribution results for finitely many tile orientations
Equidistribution results for infinitely many tile orientations
Implications for diffraction spectra and dynamical systems
Abstract
Two results about equidistribution of tile orientations in primitive substitution tilings are stated, one for finitely many, one for infinitely many orientations. Furthermore, consequences for the associated diffraction spectra and the dynamical systems are discussed.
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