Self-similar resistive circuits as fractal-like structures

TL;DR

This paper investigates resistive circuits arranged in fractal-like, self-similar patterns, analyzing their properties and specific examples such as Sierpinski configurations, revealing scale invariance and fractal characteristics.

Contribution

It introduces a definition of self-similar resistive circuits based on fractal concepts and explores their general properties and specific fractal-like resistor arrangements.

Findings

Resistive circuits exhibit self-similarity and scale invariance.

Examples include self-similar series, tree-like networks, and Sierpinski configurations.

Properties of these fractal-like circuits are systematically analyzed.

Abstract

In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski's configurations with resistors.