Three-dimensional Apollonian packing with random distribution of initially prepacked spheres is investigated. The computer simulation model with specially designed changing range genetic algorithm was developed to estimate the fractal dimensions of Apollonian packing of spherical particles. The fractal dimensions corresponding to the packing degree and porosity were calculated for a large range of spherical particles (in the order of millions). The result obtained provides an experimental proof of a lower bound of the fractal dimension analytically found by [3] (Aste, Phys. Rev. E, 1996; 53: 2571). The Society of Powder Technology Japan. Published by Elsevier B.V. on behalf of The Society of Powder Technology Japan.