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Quasicrystallic tilings and projection method. (English. Russian original) Zbl 1069.37012

J. Math. Sci., New York 121, No. 3, 2393-2400 (2004); translation from Zap. Nauchn. Semin. POMI 283, 178-192 (2001).
Summary: Basic notions related to quasiperiodic tilings and Delone sets in Euclidean space are discussed. It is shown how the cut and project method of constructing them is used to calculate their spectra. Special attention is paid to self-similar tilings and the way one can obtain one-dimensional substitutional tilings by the projection scheme.

MSC:

37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
28A80 Fractals
52C23 Quasicrystals and aperiodic tilings in discrete geometry
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