Finite-resolution effects on the logarithm-of-the-current distribution in fractal structures

The logarithm-of-the-current distributions n(lni) in a number of regular fractal models are compared with the corresponding distributions on bond-diluted random resistor networks at the percolation threshold. In the regular fractal model of Mandelbrot and Given we find that this distribution, when viewed at finite resolution, has an ${\mathit{i}}^{\gamma }$ shape over a very wide range (i.e., over many orders of magnitude of i). This agrees with the shape recently found for this distribution in the case of a random resistor network at percolation. Some other regular fractals which we considered do not exhibit this type of behavior.