IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v97y2024i8d10.1140_epjb_s10051-024-00750-z.html
   My bibliography  Save this article

Fractality in resistive circuits: the Fibonacci resistor networks

Author

Listed:
  • Petrus H. R. Anjos

    (Universidade Federal de Catalão)

  • Fernando A. Oliveira

    (Universidade Federal Fluminense
    Universidade de Brasília)

  • David L. Azevedo

    (Universidade de Brasília)

Abstract

We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show that the sequence of the network’s equivalent resistance converges uniformly in the parameter $$\alpha =\frac{r_2}{r_1} \in [0,+\infty )$$ α = r 2 r 1 ∈ [ 0 , + ∞ ) , where $$r_1$$ r 1 and $$r_2$$ r 2 are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences. Graphical abstract

Suggested Citation

  • Petrus H. R. Anjos & Fernando A. Oliveira & David L. Azevedo, 2024. "Fractality in resistive circuits: the Fibonacci resistor networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(8), pages 1-10, August.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:8:d:10.1140_epjb_s10051-024-00750-z
    DOI: 10.1140/epjb/s10051-024-00750-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/s10051-024-00750-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/s10051-024-00750-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Costa, I.V.L. & Vainstein, M.H. & Lapas, L.C. & Batista, A.A. & Oliveira, F.A., 2006. "Mixing, ergodicity and slow relaxation phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(1), pages 130-134.
    2. J. H. Asad & A. Sakaji & R. S. Hijjawi & J. M. Khalifeh, 2006. "On the resistance of an infinite square network of identical resistors – Theoretical and experimental comparison," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 52(3), pages 365-370, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gutiérrez, Caracé & Gancio, Juan & Cabeza, Cecilia & Rubido, Nicolás, 2021. "Finding the resistance distance and eigenvector centrality from the network’s eigenvalues," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).

    More about this item

    Statistics

    Access and download statistics

    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:spr:eurphb:v:97:y:2024:i:8:d:10.1140_epjb_s10051-024-00750-z. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.