1. A method of algorithmically simulating the transportation of particles through a medium, comprising the steps: a) establishing a set of initial particle and environmental conditions; b) creating a computational grid system of voxels from a physical object or system; c) establishing a plurality of ray sets of particle distributions with a computational algorithm; d) using ray sets and appropriate integration kernel to determine transport multipliers; e) initiating the simulated transportation of particles by applying a plurality of discrete particle distributions within voxel interaction tallies and/or upon voxel tally surfaces; f) applying the transport multipliers for transporting discrete particle tallies from the first plurality of voxels to a second plurality of voxels; g) continuing the particle tallies in voxels as the ray sets of particle distributions sequentially transport through the grid system of voxels until a predetermined limit is attained; h) compiling the particle interaction tallies from within computer memory locations and applying the interaction model to determine scattering, state and accumulated interactions over a time epoch or generation; i) repeating steps (f-h) until interaction reaction rates and/or generational eigenvalue substantially converge; and j) computationally producing an output indicative of the simulated particle transport.