Modelling porous structures by repeated Sierpinski carpets

Porous materials such as sedimentary rocks often show a fractal character at certain length scales. Deterministic fractal generators, iterated upto several stages and then repeated periodically, provide a realistic model for such systems. On the fractal, diffusion is anomalous, and obeys the law 〈r2〉∼t2/dw, where 〈r2〉 is the mean square distance covered in time t and dw>2 is the random walk dimension. The question is: How is the macroscopic diffusivity related to the characteristics of the small scale fractal structure, which is hidden in the large-scale homogeneous material? In particular, do structures with same dw necessarily lead to the same diffusion coefficient at the same iteration stage? The present paper tries to shed some light on these questions.