Fractality in resistive circuits: the Fibonacci resistor networks

Petrus H. R. Anjos (), Fernando A. Oliveira () and David L. Azevedo ()
Additional contact information
Petrus H. R. Anjos: Universidade Federal de Catalão
Fernando A. Oliveira: Universidade Federal Fluminense
David L. Azevedo: Universidade de Brasília

The European Physical Journal B: Condensed Matter and Complex Systems, 2024, vol. 97, issue 8, 1-10

Abstract: 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

Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1140/epjb/s10051-024-00750-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/s10051-024-00750-z

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().