Fractality in resistive circuits: The Fibonacci resistor networks

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Détails bibliographiques
Auteurs principaux:	Anjos, Petrus H. R. dos, Oliveira, Fernando A., Azevedo, David L.
Format:	Preprint
Publié:	2024
Sujets:	Statistical Mechanics
Accès en ligne:	Acceder al recurso
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author	Anjos, Petrus H. R. dos Oliveira, Fernando A. Azevedo, David L.
author_facet	Anjos, Petrus H. R. dos Oliveira, Fernando A. Azevedo, David L.
contents	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 $α=\frac{r_2}{r_1} \in [0,+\infty)$, where $r_1$ and $r_2$ 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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2409_00229
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Fractality in resistive circuits: The Fibonacci resistor networks Anjos, Petrus H. R. dos Oliveira, Fernando A. Azevedo, David L. Statistical Mechanics 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 $α=\frac{r_2}{r_1} \in [0,+\infty)$, where $r_1$ and $r_2$ 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.
title	Fractality in resistive circuits: The Fibonacci resistor networks
topic	Statistical Mechanics
url	https://arxiv.org/abs/2409.00229

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