Numerical simulations of vein evolution contribute to a better understanding of processes involved in their formation and possess the potential to provide invaluable insights into the rock deformation history and fluid flow pathways. The primary aim of the present article is to investigate the influence of a “realistic” boundary condition, i.e. an algorithmically generated “fractal” surface, on the vein evolution in 3-D using a thermodynamically consistent approach, while explaining the benefits of accounting for an extra dimensionality. The 3-D simulation results are supplemented by innovative numerical post-processing and advanced visualization techniques. The new methodologies to measure the tracking efficiency demonstrate the importance of accounting the temporal evolution; no such information is usually accessible in field studies and notoriously difficult to obtain from laboratory experiments as well. The grain growth statistics obtained by numerically post-processing the 3-D computational microstructures explain the pinning mechanism which leads to arrest of grain boundaries/multi-junctions by crack peaks, thereby, enhancing the tracking behavior.