  In the present contribution three means of measuring the geometrical and
topological complexity of photons' paths in random media are proposed. This is
realized by investigating the behavior of the average crossing number, the mean
writhe, and the minimal crossing number of photons' paths generated by Monte
Carlo (MC) simulations, for different sets of optical parameters. It is
observed that the complexity of the photons' paths increases for increasing
light source/detector spacing, and that highly "knotted" paths are formed. Due
to the particular rules utilized to generate the MC photons' paths, the present
results may have an interest not only for the biomedical optics community, but
also from a pure mathematical point of view.
