2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/151721The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot transformation, leading to a fractal behavior of the percolation probability in the complex plane. The hierarchical chains of impedances, reducing to a nonlinear mapping of the impedance space onto itself, are studied. An infinite continuation of the procedure leads to a fixed point. It is shown that the number of steps required to reach a neighborhood of this point has a fractal distribution.LaTeX file and 2 PostScripts with 6 fig.Disordered Systems and Neural Networkstext