Self-similar ornaments obtained from girih tiles
نویسندگان
چکیده
منابع مشابه
Medieval Islamic Architecture, Quasicrystals, and Penrose and Girih Tiles: Questions from the Classroom
Tiling Theory studies how one might cover the plane with various shapes. Medieval Islamic artisans developed intricate geometric tilings to decorate their mosques, mausoleums, and shrines. Some of these patterns, called girih tilings, first appeared in the 12 Century AD. Recent investigations show these medieval tilings contain symmetries similar to those found in aperiodic Penrose tilings firs...
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Let b ≥ 2 be an integer base, D = {0, d1, · · · , db−1} ⊂ Z a digit set and T = T (b,D) the set of radix expansions. It is well known that if T has nonvoid interior, then T can tile R with some translation set J (T is called a tile and D a tile digit set). There are two fundamental questions studied in the literature: (i) describe the structure of J ; (ii) for a given b, characterize D so that ...
متن کاملON ONE-DIMENSIONAL SELF-SIMILAR TILINGS AND pq-TILES
Let b ≥ 2 be an integer base, D = {0, d1, · · · , db−1} ⊂ Z a digit set and T = T (b,D) the set of radix expansions. It is well known that if T has nonvoid interior, then T can tile R with some translation set J (T is called a tile and D a tile digit set). There are two fundamental questions studied in the literature: (i) describe the structure of J ; (ii) for a given b, characterize D so that ...
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A self a ne tile in R is a set T of positive Lebesgue measure satisfying A T d D T d where A is an expanding n n real matrix with j det A j m an integer and D fd dmg R n a set of m digits Self a ne tiles arise in many contexts including radix expansions fractal geometry and the construction of compactly sup ported orthonormal wavelet bases of L R They are also studied as interesting tiles In th...
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ژورنال
عنوان ژورنال: Acta Crystallographica Section A Foundations of Crystallography
سال: 2008
ISSN: 0108-7673
DOI: 10.1107/s0108767308094695