Complex quasiperiodic self-similar tilings: their parameterization, boundaries, complexity, growth and symmetry

被引：13

作者：

Shutov, A. V. ^{[1
]}

Maleev, A. V. ^{[1
]}

Zhuravlev, V. G. ^{[1
]}

机构：

[1] Vladimir State Humanitarian Univ, Dept Phys, Vladimir 600024, Russia

来源：

ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES | 2010年 / 66卷

关键词：

BY-LAYER GROWTH; DYNAMICAL-SYSTEMS; RAUZY; CONSTRUCTION;

D O I：

10.1107/S0108767310006616

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

A class of quasiperiodic tilings of the complex plane is discussed. These tilings are based on beta-expansions corresponding to cubic irrationalities. There are three classes of tilings: Q(3), Q(4) and Q(5). These classes consist of three, four and five pairwise similar prototiles, respectively. A simple algorithm for construction of these tilings is considered. This algorithm uses greedy expansions of natural numbers on some sequence. Weak and strong parameterizations for tilings are obtained. Layerwise growth, the complexity function and the structure of fractal boundaries of tilings are studied. The parameterization of vertices and boundaries of tilings, and also similarity transformations of tilings, are considered.

引用

页码：427 / 437

页数：11

共 36 条

[21] RAUZY G, 1982, B SOC MATH FR, V110, P147
[22] Schlottmann M, 1998, QUASICRYSTALS DISCRE, P247
[23] Quasiperiodic plane tilings based on stepped surfaces
Shutov, A. V.
Maleev, A. V.
[J]. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES, 2008, 64 : 376 - 382
[24] SHUTOV AV, 2003, TCHEBYSHEVSKIY SBORN, V4, P82
[25] Self-affine tiling via substitution dynamical systems and Rauzy fractals
Sirvent, VF
Wang, Y
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2002, 206 (02) : 465 - 485
[26] THURSTON WP, 1990, GROUPS TILINGS FINIT
[27] Quasi-periods of layer-by-layer growth of Rauzy tiling
Zhuravlev, V. G.
Maleev, A. V.
[J]. CRYSTALLOGRAPHY REPORTS, 2008, 53 (01) : 1 - 8
[28] Complexity function and forcing in the 2D quasi-periodic rauzy tiling
Zhuravlev, V. G.
Maleev, A. V.
[J]. CRYSTALLOGRAPHY REPORTS, 2007, 52 (04) : 582 - 588
[29] Layer-by-layer growth of quasi-periodic Rauzy tiling
Zhuravlev, V. G.
Maleev, A. V.
[J]. CRYSTALLOGRAPHY REPORTS, 2007, 52 (02) : 180 - 186
[30] Similarity symmetry of a 2D quasi-periodic Rauzy tiling
Zhuravlev, V. G.
Maleev, A. V.
[J]. CRYSTALLOGRAPHY REPORTS, 2009, 54 (03) : 370 - 378

← 1 2 3 4 →