Fractal-type relations and extensions suitable for systems of evolving polycrystalline microstructures

We report on two possible physically justified situations concerning the evolution of polycrystalline microstructures. The first is an observation that a polycrystalline microstructure formation process, considered as a random walk in the space of the crystallites’ sizes, can be equivalent to the anomalous kinetic problem in a continuum percolation space. The second, in turn, regards some extension of the random walk process while occurring on a fractal substrate and/or when a single grain boundary can presumably be treated as a random walk trajectory, i.e. a situation quite acceptable when dealing with, e.g. quasicrystals. One may find possible applications of the modeling offered in the areas of biophysics and physical metallurgy.