A new multidimensional slow continued fraction algorithm and stepped surface

2013/10/29 by Maki Furukado, Shunji Ito, Furukado, Maki +7
Computer Science · Mathematics · #11A55 (Primary) #11Y16 #11Y65 #37B10 (Secondary) #Cellular Automata and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT #msc:11A55 #msc:11Y16 #msc:11Y65 #msc:37B10 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1310.7781

41 pages, 9 figures

arxiv created 2013/10/29 · openalex publication_date 2013/10/29 · arxiv updated 2013/10/30 · openalex created_date 2022/02/24 · openalex updated_date 2026/07/28

Abstract

We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling substitutions) for any stepped surface for any cubic direction.

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