Title: Self-similar resistive circuits as fractal-like structures,
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.