DC conductive percolation of 2-D fractal random network

We report the numerical investigation of DC conductive percolation in a two-dimensional (2-D) random fractal resistor network. The network is configurated by covering a deterministic fractal of Sierpinski carpet and occupied with low- or high-value resistors. The percolation current is calculated straightforwardly and exactly by solving the linear equations of Kirchhoffʹs law. The DC percolation current below and above threshold pc exhibits a scaling behavior in four ranges. Due to the iteration of setting low R resistors in Sierpinski carpet, the percolation threshold probability pc shifts from 0.5 to lower value for higher level iterations. We observed that the fractal constructed in network changes the percolation property, and this results in a bifurcation curve of threshold. This effect gives an explanation for the usually observed natural phenomena, such as arc current or flicker noise. Our result reveals good agreement with experimental observation.