Earthquake-producing fault systems like the San Andreas fault in California show self-similar structural variation¹; earthquakes cluster in space, leaving aseismic gaps between clusters. Whether gaps represent overdue earthquakes or signify diminished risk is a question with which seismic-hazard forecasters wrestle^1,2,3,4,5. Here I use spectral analysis of the spatial distribution of seismicity along the San Andreas fault (for earthquakes that are at least 2 in magnitude), which reveals that it obeys a power-law relationship, indicative of self-similarity in clusters across a range of spatial scales. To determine whether the observed clustering of earthquakes is the result of a heterogeneous stress distribution, I use a finite-element method to simulate the motion of two rigid blocks past each other along a model fault surface that shows three-dimensional complexity on the basis of mapped traces of the San Andreas fault. The results indicate that long-term slip on the model fault generates a temporally stable, spatially variable distribution of stress that shows the same power-law relationship as the earthquake distribution. At the highest rates of San Andreas fault slip (40 mm yr⁻¹), stress patterns produced are stable over a minimum of 25,000 years before the model fault system evolves into a new configuration. These results suggest that although gaps are not immune to rupture propagation they are less likely to be nucleation sites for earthquakes.