IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p742-d1349512.html
   My bibliography  Save this article

The Ruler Sequence Revisited: A Dynamic Perspective

Author

Listed:
  • Juan Carlos Nuño

    (Department of Applied Mathematics, Universidad Politécnica de Madrid, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Juan Carlos Nuño & Francisco J. Muñoz, 2024. "The Ruler Sequence Revisited: A Dynamic Perspective," Mathematics, MDPI, vol. 12(5), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:742-:d:1349512
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/742/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/5/742/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:742-:d:1349512. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.