Abstract
Fractals play a central role in several areas of modern physics and mathematics. 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.
Highlights
Fractality is a relatively recent but powerful concept that permeates much of physics and mathematics
Fractals are used in realist modelings of nature
Quoting Benoıt Mandelbrot [8], “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”
Summary
Fractality is a relatively recent but powerful concept that permeates much of physics and mathematics. A basic characteristic of this structure is scale invariance, that is, the fractal pattern remains the same with any magnification Physics oriented works involving self-similar resistive circuits include the investigation of resistance properties of Sierpinski triangle fractal networks [16,17,18] and binary tree circuits [19], among several other fractal patterns. A general definition for self-similar resistive circuits is proposed and explored. We derive a condition to characterize the calculation of the equivalent resistance of a self-similar circuit as a fixed-point problem.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
