Percolation transition into random-Sierpinski-carpets

Optical and electrical properties of inhomogeneous media, strongly depend on the percolating properties of one of the component. In many cases, inhomogeneous media present fractal structures near and at the percolation threshold, and in general, transport properties exhibit a very special behaviour in this concentration range. In contrast with the theoretical simulations, the scale invariance ratio of the real systems (granular metal films, porous media…) is limited, which has a direct influence on the percolating properties of the clusters. The real space renormalization method is used to investigate the site percolation transition into rando,-Sierpinsky-carpets with various scale invariance ratio. It is shown that the fixed point of the renormalization group (i.e. the percolation threshold) is not unique but depends on the number of segmentation steps used to generate the fractal.