Neither the Omori type of clustering prior to and following large earthquakes nor the Gutenberg-Richter distribution are reproducible by present continuous models. Discrete models, on the other hand, give rise to more complex and closer to realistic earthquake clustering. The objective of this study is twofold: to explore the consequences of spatial discreteness on the distribution in time and space of earthquake activity on a fault governed by rate-and-state friction and to examine the effect of interaction between seismic slip and aseismic creep on aftershock sequences. To that end we model a long, vertical, two-dimensional strike-slip fault that is governed by rate- and state-dependent friction and is embedded in a three-dimensional elastic half-space. Quasi-dynamic motion on the fault is driven by steady displacement applied below the fault and at distance W/2 on either side of the fault plane. The model is said to be spatially discrete in that the computational cells are oversized with respect to the critical length scale that is implied by the friction law. The model reproduces some of the characteristics of natural seismicity, including the nonperiodic recurrence times and the Omori type of clustering prior to and following large earthquakes. It also produces a wide range of earthquake magnitudes but with a ratio of small to large earthquakes that is in excess with respect to what is inferred form natural catalogs. We examined the effect of a stress step applied on the creeping portions of the model and confirmed that aftershock sequences resulting from stress relaxation on creeping segments decay asymptotically to 1/time. Finally, we discuss fundamental differences between seismicity models employing rate-and-state friction and those employing static/kinetic friction.