Multidimensional paperfolding systems

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

Research output: Contribution to journalArticlepeer-review

4 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 languageEnglish
Pages (from-to)123-130
Number of pages8
JournalActa Crystallographica Section A: Foundations of Crystallography
Volume69
Issue number2
DOIs
StatePublished - 1 Mar 2013

Keywords

  • multidimensional paperfolding structure
  • recursion

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