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Cut-and-Project Schemes for Pisot Family Substitution Tilings

Cut-and-Project Schemes for Pisot Family Substitution Tilings
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Aperiodic set of tiles and cut and project method

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Cut-and-project graphs and other complexes

Theoretical Computer Science, 2021
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Cut-and-project sets and their -duals

Philosophical Magazine, 2007
Motivated by approximation and real analysis, Meyer introduced model sets (also called cut-and-project sets), which are used as mathematical models of quasicrystals. In his study, a central role was played by the ϵ-dual. The ϵ-dual of a lattice is the reciprocal lattice, and that of a cut-and-project set is contained by the diffraction pattern.
Y. Akama, S. Iizuka
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Cut-and-project sequences and substitution rules

Ferroelectrics, 2001
Abstract We consider infinite words in a 3-letter alphabet which arise from the cut-and-project scheme based on quadratic unitary Pisot numbers. Such sequences may be considered as ternary generalizations of classical Sturmian sequences. We describe the complexity of such sequences and give a condition under which these generalized Sturmian sequences ...
Zuzana Masáková, Edita Pelantová
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Inflation centres of the cut and project quasicrystals

Journal of Physics A: Mathematical and General, 1998
Cut-and-project quasicrystals which display golden ratio inflation symmetries are investigated. The subclass with convex window is exhaustively described with respect to the possible inflation centres, both internal and external to the point set. Also, the possible inflation factors themselves are determined and found to form a 1D quasicrystal.
Masáková, Zuzana, Patera, Jiří, Pelantová, Edita   +2 more
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Characterization of Cut-and-Project Sets Using a Binary Operation

Letters in Mathematical Physics, 2000
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Masáková, Zuzana, Pelantová, Edita, Svobodová, Milena   +2 more
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Two‐scale cut‐and‐projection convergence; homogenization of quasiperiodic structures

Mathematical Methods in the Applied Sciences, 2017
We demonstrate how the problem of finding the effective property of quasiperiodic constitutive relations can be simplified to the periodic homogenization setting by transforming the original quasiperiodic material structure to a periodic heterogeneous material in a higher dimensional space.
Wellander, Niklas, Guenneau, Sébastien, Cherkaev, Elena   +2 more
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S-convexity and cut-and-project sets

Ferroelectrics, 2001
Abstract Cut-and-project sets with convex acceptance window based on irrationalities τ = 1/2(1 + √5), β = 1 + √2, μ = 2 + √3 are models for experimentally observed quasicrystals-materials with diffraction patterns consisting of sharp Bragg peaks in crystalographically disallowed patterns.
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