A dynamical system under extreme physical disorder has the tendency to evolve toward the equilibrium state characterized by an inverse power law power spectrum. In this paper, a practical, implementable, three-dimensional model is proposed for the random media formed by a multimaterials mixture under such a power spectrum using a randomized form of the Weierstrass function, its extension covering the white noise, and partial volume pairings of constituent materials. The proposed model is implemented in the SOLOMON Monte Carlo solver with delta tracking. Two sets of numerical results are shown using the JENDL-4 nuclear data libraries. First, the uncertainty of the neutron effective multiplication factor (keff) due to the inherent uncertainty in the formation of random media is shown for a randomized version of the Bigten core in the International Criticality Safety Benchmark Evaluation Project (ICSBEP). Second, the influence of the exponent of the power spectrum on the uncertainty of keff is evaluated for a randomized version of the Topsy core in the ICSBEP.
