Menger Sponge Models

Menger Sponge (in 3D) and Sierpiński CarpetSierpiński carpet (in 2D) are the most useful fractal modelsFractal model of the rocks’ pore spacePore space. Sections 5.1 and 5.2 treat these models, their combinatorial and topological properties. Random and multifractalMultifractal generalizations are discussed in Sect. 5.3, where the permeabilityPermeability of these models is also studied. A mathematical Appendix 5.4 introduces a useful measure, lacunarityLacunarity, a tool to distinguish between textures of the same fractal dimension but different geometry. Petrophysical applications are summarized in Table 5.1.