Fractions, Functions and Folding. A Novel Link between Continued Fractions, Mahler Functions and Paper Folding
Number Theory
2021-08-27 v1 Combinatorics
Complex Variables
Abstract
Repeatedly folding a strip of paper in half and unfolding it in straight angles produces a fractal: the dragon curve. Shallit, van der Poorten and others showed that the sequence of right and left turns relates to a continued fraction that is also a simple infinite series. We construct a Mahler function from two functions of Dilcher and Stolarsky with similar properties. It produces a predictable irregular continued fraction that admits a regular continued fraction and a shape resembling the dragon curve. Furthermore, we discuss numerous variations on this theme.
Keywords
Cite
@article{arxiv.2108.11382,
title = {Fractions, Functions and Folding. A Novel Link between Continued Fractions, Mahler Functions and Paper Folding},
author = {Joris Nieuwveld},
journal= {arXiv preprint arXiv:2108.11382},
year = {2021}
}
Comments
57 pages, 7 figures. Master's Thesis