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arXiv · 2409.00229

Fractality in resistive circuits: The Fibonacci resistor networks

Petrus H. R. dos Anjos·Fernando A. Oliveira·David L. Azevedo
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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 $\alpha=\frac{r_2}{r_1} \in [0,+\infty)$, 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.

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Petrus H. R. dos Anjos, Fernando A. Oliveira, David L. Azevedo. 2024-08-30. Fractality in resistive circuits: The Fibonacci resistor networks. https://doi.org/10.1140/epjb%2Fs10051-024-00750-z

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