Multidimensional paperfolding systems
International Union of Crystallography, 2013
Acta Crystallographica Section A
Volume 69, Issue 2, pages 123–130, March 2013
How to Cite
Ben-Abraham, S. I., Quandt, A. and Shapira, D. (2013), Multidimensional paperfolding systems. Acta Crystallographica Section A, 69: 123–130. doi: 10.1107/S010876731204531X
- multidimensional paperfolding structure
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.