Up to the present time, ground-motion calculations for future earthquakes have almost exclusively been made from kinematic models. However, dynamic faulting models offer many benefits over kinematic models, including the assurance the faulting models obey at least the general rules of elastodynamics and friction and contain a natural relationship between stress drop, slip, rise time, and rupture velocity. Dynamic models also offer insight into the physics of the rupture and slip processes and can show how these processes lead to patterns of ground motion. In the current work, we use the 3D finite-difference method and a suite of stochastic stress patterns, with variable assumptions on strength and stress inhomogeneity, to investigate two issues: (1) the effect of assumptions about stress pattern on the evolution of rupture and slip on the fault, and (2) the effect of these assumptions on the resultant ground motion. We find that stress drop has a complicated relationship with slip, rise time, and rupture velocity, especially in faults with strongly heterogeneous strength. We also find that these inhomogeneous-strength faults can produce highly inhomogeneous slip, even without any form of frictional restrengthening at healing time. Finally, we find that smoother strength models produce a better fit than the coarse models to the directivity pulse often observed on the surface. The results help to shed light on the transition of the faulting system between locally controlled and more globally controlled rupture and also show how dynamic models may be used to generate ground-motion estimates for seismic hazard calculations.