A computer simulation was developed to simulate electron-beam-induced deposition (EBID). Simulated growth produced high-aspect-ratio, nanoscale pillar structures by simulating a stationary Gaussian electron beam. The simulator stores in memory the spatial and temporal coordinates of deposited atoms in addition to the type of electron, either primary (PE), back-scattered (BSE), or secondary (SE), that induced its deposition. The results provided in this paper apply to tungsten pillar growth by EBID on a tungsten substrate from WF6 precursor, although the simulation may be applied to any substrate-precursor set. The details of the simulation are described including the Monte Carlo electron-solid interaction simulation used to generate scattered electron trajectories and SE generation, the probability of molecular dissociation of the precursor gas when an electron traverses the surface, and the gas dynamics which control the surface coverage of the WF6 precursor on the substrate and pillar surface. In this paper, three specific studies are compared: the effects of beam energy, mass transport versus reaction-rate-limited growth, and the effects of surface diffusion on the EBID process.