  We propose an approximate reconstruction of random heterogeneous
microstructures using the two-exponent power-law (TEPL). This rule originates
from the entropic descriptor (ED) that is a multi-scale measure of spatial
inhomogeneity for a given microstructure. A digitized target sample is a cube
of linear size L in voxels. Then, a number of trial configurations can be
generated by a model of overlapping spheres of a fixed radius, which are
randomly distributed on a regular lattice. The TEPL describes the averaged
maximum of the ED as a function of the phase concentration and the radius.
Thus, it can be used to determine the radius. The suggested approach is tested
on surrogate samples of ceramic and carbonate. In each of the cases, fifty
low-cost trials provided a few good enough candidates to a selection of the
optimal reconstruction. When a better accuracy is planned, the final
reconstructions can serve as the starting configurations. Then, the resulting
reconstructions should be competitive indeed to those starting with random
configurations.
