2021/08/25 by Joris Nieuwveld, Nieuwveld, Joris
Computer Science · Engineering · #11J70 (Primary) 11B85 (Secondary) #Advanced Materials and Mechanics #Algorithms and Data Compression #Cellular Automata and Applications #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2108.11382
openalex publication_date 2021/08/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Repeatedly folding a strip of paper in half and unfolding it in straight\nangles produces a fractal: the dragon curve. Shallit, van der Poorten and\nothers showed that the sequence of right and left turns relates to a continued\nfraction that is also a simple infinite series. We construct a Mahler function\nfrom two functions of Dilcher and Stolarsky with similar properties. It\nproduces a predictable irregular continued fraction that admits a regular\ncontinued fraction and a shape resembling the dragon curve. Furthermore, we\ndiscuss numerous variations on this theme.\n