Multidimensional paperfolding systems

Shelomo I. Ben-Abraham; Alexander Quandt; Dekel Shapira

doi:10.1107/S010876731204531X

Multidimensional paperfolding systems

Shelomo I. Ben-Abraham, Alexander Quandt, Dekel Shapira

Department of Physics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	123-130
Number of pages	8
Journal	Acta Crystallographica Section A: Foundations of Crystallography
Volume	69
Issue number	2
DOIs	https://doi.org/10.1107/S010876731204531X
State	Published - 1 Mar 2013

Keywords

multidimensional paperfolding structure
recursion

ASJC Scopus subject areas

Structural Biology

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1107/S010876731204531X

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AB - 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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Multidimensional paperfolding systems

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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