Aperiodic Tilings in Higher Dimensions
نویسندگان
چکیده
منابع مشابه
Aperiodic Tilings in Higher Dimensions
We show that in dimensions d > 3 , aperiodic tilings can naturally avoid more symmetries than just translations.
متن کاملAperiodic Tiliings in Higher Dimensions*
We show that in dimensions d 3, aperiodic tilings can naturally avoid more symmetries than just translations.
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The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the 2n-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmet...
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In this paper we present a construction of Kari-Culik aperiodic tile set — the smallest known until now. With the help of this construction, we prove that this tileset has positive entropy. We also explain why this result was not expected.
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An aperiodic tiling is one which uses a nite set of prototiles to tile space such that there is no translational symmetry within any one tiling. These tilings are of interest to researchers in the natural sciences because they can be used to model and understand quasicrystals, a recently-discovered type of matter which bridges the gap between glass, which has no regular structure, and crystals,...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.2307/2161105