In Part I we considered continuous in scale cascade processes which were spatially continuous these are needed for modeling many geofields In this second part we consider the effects of spatial discretization this allows us to make numerical simulations We show how to correct the simulations for the leading finite size effects for both space and (causal) space-time processes The resulting processes have significantly improved small scale statistical properties in practice it can lead to great savings in computer time and memory usage In an appendix we give a Mathematica code for the corresponding space-time simulations (C) 2010 Elsevier Ltd All rights reserved