Scaling accounts for a sort of dependence between local (microscopic, or very small) and global (macroscopic) properties of a system in question. Fractal dimension and its generalizations, as critical exponents in a power-law scaling, have been chosen as a tool in the reconsideration of a mass transport through membranes, and in the process of casting (DLA membranes). The passage from the diffusion on the prototype structures (e.g. Sierpinski gasket) to the diffusion on real structures has also been shown.