  We consider simulation of spatially one-dimensional space-time fractional
diffusion. Whereas in an earlier paper of ours we have developed the basic
theory of what we call parametric subordination via three-fold splitting
applied to continuous time random walk with subsequent passage to the diffusion
limit, here we go the opposite way. Via Fourier-Laplace manipulations of the
relevant fractional partial differential equation of evolution we obtain the
subordination integral formula that teaches us how a particle path can be
constructed by first generating the operational time from the physical time and
then generating in operational time the spatial path. By inverting the
generation of operational time from physical time we arrive at the method of
parametric subordination. Due to the infinite divisibility of the stable
subordinator, we can simulate particle paths by discretization where the
generated points of a path are precise snapshots of a true path. By refining
the discretization more and more fine details of a path become visible.
