title: Multidimensional paperfolding systems.
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.
authors: Department of Physics, Ben-Gurion University of the Negev, IL-84105 Beer-Sheba, Israel. benabr@bgu.ac.il
authors: Shelomo I
authors: SI
authors: Ben-Abraham
authors: Alexander
authors: A
authors: Quandt
authors: Dekel
authors: D
authors: Shapira
keywords: multidimensional paperfolding structure; recursion