Multidimensional "Paperfolding" Structures - Three and Four Dimensions

Abstract

We recapitulate our previously developed recursive algorithm for creating paperfolding structures in arbitrary dimensions. Here we explain and apply it specically to three and four dimensions. We visualize the results by suitable projections. We also explicitly enumerate the number of folds in the rst four generations of the recursion.We conjecture (without proof ) that the Fourier spectrum of the structures is pure point (the Bragg peaks).

Multidimensional color codes for chair tilings

“…The work reported in this paper is part of a project generalizing one-dimensional sequences and two-dimensional structures to higher dimensions (Ben-Abraham & Quandt, 2011;Ben-Abraham et al, 2013, 2014Lee et al, 2016). A preliminary short report on the present subject was published in the Proceedings of ICQ 13 (Flom & Ben-Abraham, 2017).…”