Multidimensional paperfolding systems.

IF 1.8 4区材料科学

Acta Crystallographica Section A Pub Date : 2013-03-01 Epub Date: 2013-01-08 DOI:10.1107/S010876731204531X

Shelomo I Ben-Abraham, Alexander Quandt, Dekel Shapira

引用次数: 4

Abstract

Algorithms for constructing aperiodic structures produce templates for the nanofabrication of arrays for applications in photonics, phononics and plasmonics. Here a general multidimensional recursion rule is presented for the regular paperfolding structure by straightforward generalization of the one-dimensional rule. As an illustrative example the two-dimensional version of the paperfolding structure is explicitly constructed, its symbolic complexity referred to rectangles computed and its Fourier transform shown. The paperfolding structures readily yield novel 'paperfolding' tilings. Explicit formulas are put forward to count the number of folds in any dimension. Finally, possible generalizations of the dragon curve are discussed.

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多维折纸系统。

构造非周期结构的算法为光子学、声子学和等离子体学中应用的纳米阵列制造提供了模板。本文通过对一维规则的简单推广，给出了规则折纸结构的一般多维递归规则。作为一个说明性的例子，二维版本的折纸结构是明确构建的，其符号复杂性指的矩形计算和其傅里叶变换显示。折纸结构很容易产生新颖的“折纸”瓷砖。提出了计算任意维度上的折叠数的显式公式。最后，讨论了龙曲线的可能推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A 化学-晶体学

自引率

11.10%

发文量

审稿时长

3 months

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.