The Ruler Sequence Revisited: A Dynamic Perspective

Juan Carlos Nuño () and Francisco J. Muñoz
Additional contact information
Juan Carlos Nuño: Department of Applied Mathematics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Francisco J. Muñoz: Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, ESCET, Universidad Rey Juan Carlos, Móstoles, 28933 Madrid, Spain

Mathematics, 2024, vol. 12, issue 5, 1-14

Abstract: The Ruler function or the Gros sequence is a classical infinite integer sequence that underlies some interesting mathematical problems. In this paper, we provide four new problems containing this type of sequence: (i) demographic discrete dynamical automaton, (ii) the middle interval Cantor set, (iii) construction by duplication of polygons and (iv) the horizontal visibility sequence at the accumulation point of the Feigenbaum cascade. In all of them, the infinite sequence is obtained through a recursive procedure of duplication. The properties of the ruler sequence, in particular, those relating to recursiveness and self-containing, are used to achieve a deeper understanding of these four problems. These new representations of the ruler sequence could inspire new studies in the field of discrete mathematics.

Keywords: ruler sequence; cantor set; Feigenbaum cascade; cellular automata; regular polygons (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/5/742/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/5/742/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:5:p:742-:d:1349512

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().