Previous studies noted situations with simple networks of fractured media where dispersion was complex. Certain network geometries provided principal directions of spreading at angles to the direction of mean flow and occasions where transverse spreading greatly exceeded longitudinal spreading. This article is concerned with understanding this complex dispersion in the context of more variable networks and to evaluate the scaling between dispersion and characteristics of the network. The approach involves modeling flow and particle transport through networks consisting of equally spaced finite fractures. Simulation trials examined how changes to the orientation of the overall network, fracture aperture, fracture connectivity, and fracture length influenced mass transport. With these geometries, particle spreading was due to a grid orientation effect and variability related to apertures and connectivity. The grid orientation effect inherently gives rise to the complex dispersion described in previous work. Spreading caused by variability in aperture and connectivity produces the more familiar, elliptical pattern of spreading. In the various model trials we created situations where either or both of these spreading mechanisms could dominate. When both grid orientation and heterogeneity effects were comparable, particle swarms took on a curious hybrid shape reflecting the outcome of two different spreading mechanisms. With sufficient heterogeneity the grid orientation effect was swamped and disappeared. As the block size increases so does transverse dispersion. Further studies are necessary to investigate whether the grid effects associated with the simplified fracture networks can be extrapolated to real fractured media.