Local rules for pentagonal quasi-crystals

DOI10.1007/BF02570695zbMath0842.52011MaRDI QIDQ1894718

Le Ty Kuok Tkhang

Publication date: 1 August 1995

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131391

zbMATH Keywords

surveylocal rulesquasi-crystalsPenrose tilings

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Discrete geometry (52C99)

Related Items (6)

Meyer's concept of quasicrystal and quasiregular sets ⋮ Weak local rules for planar octagonal tilings ⋮ Canonical projection tilings defined by patterns ⋮ No weak local rules for the \(4_p\)-fold tilings ⋮ Weak colored local rules for planar tilings ⋮ When periodicities enforce aperiodicity

Cites Work

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• Weak matching rules for quasicrystals
• Theory of matching rules for the 3-dimensional Penrose tilings
• Absence of weak local rules for the planar quasicrystalline tiling with the 8-fold rotational symmetry
• On the computational complexity and geometry of the first-order theory of the reals. I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals
• Aperiodic tiles
• Local rules for quasiperiodic tilings of quadratic 2-planes in \({\mathbb{R}{}}^ 4\)
• Complexity of deciding Tarski algebra
• The pinwheel tilings of the plane
• Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings
• Generalised 2D Penrose tilings: structural properties
• Global order from local sources
• Some aspects of the theory of quantum groups

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