The pore structure of Sierpinski carpets

In this paper, a new method is developed to investigate the pore structure of finitely and even infinitely ramified Sierpinski carpets. The holes in e very iteration stage of the carpet are described by a hole-counting polynom ial. This polynomial can be computed iteratively for all carpet stages and contains information about the distribution of holes with different areas a nd perimeters, from which dimensions governing the scaling of these quantit ies can be determined. Whereas the hole area is known to be two dimensional , the dimension of the hole perimeter may be related to the random walk dim ension.