Fractal AC circuits and propagating waves on fractals

by Eric Akkermans, Joe P. Chen, Gerald Dunne, Luke G. Rogers and Alexander Teplyaev

We extend Feynman’s analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the individual impedances inside the circuit are purely imaginary. This provides a physical setting for analyzing wave propagation of signals on fractals, by analogy with the Telegrapher’s Equation, and generalizes the real resistance metric on a fractal, which provides a measure of distance on a fractal, to complex impedances.

Arxiv Preprint version

Published version in volume Analysis, Probability and Mathematical Physics on Fractals