Multidimensional paperfolding systems. (8th January 2013)

• Record Type: Journal Article
• Authors: Ben‐Abraham, Shelomo I.; Quandt, Alexander; Shapira, Dekel
• Is Part Of: Acta crystallographica. Volume 69:Part 2(2013:Mar.)
• Page Start: 123
• Page End: 130
• Publication Date: 2013-01-08
• Subjects: Crystallography -- Periodicals; Condensed matter -- Periodicals; 530.41
• DOI: 10.1107/S010876731204531X
• Languages: English
• ISSNs: 2053-2733

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>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.</p> </abstract>