Inflation and wavelets for the icosahedral Danzer tiling
Inflation and wavelets for the icosahedral Danzer tiling
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二十面体 Danzer 平铺的膨胀和小波
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
M. Andrle
中科院分区：
文献类型：
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作者：
P. Kramer;M. Andrle
准晶体中原子的分布缺乏周期性，表现出与非晶体模块相关的点对称性。通常，它可以用由有限数量的原始瓷砖建造的准周期瓷砖来描述。五重点对称和二十面体对称的模和正则平铺允许膨胀对称。在最简单的石头膨胀情况下，任何按黄金分割数字τ缩放的原始瓷砖都可以从未缩放的原始瓷砖中打包。准晶体上支持的可观测性需要对称性适应的函数空间。我们构造了二十面体Danzer瓦片的小波基。根据欧几里得群运算的作用，明确地给出了四个Danzer原石的膨胀。通过对原型的特征函数进行与这些运算相反的么正表示，我们递归地提供了的全正交小波基。它结合了二十面体和膨胀对称性。
The distribution of atoms in quasi-crystals lacks periodicity and displays point symmetry associated with non-crystallographic modules. Often it can be described by quasi-periodic tilings on built from a finite number of prototiles. The modules and the canonical tilings of five-fold and icosahedral point symmetry admit inflation symmetry. In the simplest case of stone inflation, any prototile when scaled by the golden section number τ can be packed from unscaled prototiles. Observables supported on for quasi-crystals require symmetry-adapted function spaces. We construct wavelet bases on for the icosahedral Danzer tiling. The stone inflation of the four Danzer prototiles is given explicitly in terms of Euclidean group operations acting on . By acting with the unitary representations inverse to these operations on the characteristic functions of the prototiles, we recursively provide a full orthogonal wavelet basis of . It incorporates the icosahedral and inflation symmetry.