The problem of how fault rheology and heterogeneity interact to produce the observed scaling of earthquakes (such as the power-law moment-frequency relationship) remains largely unsolved. Rock friction experiments have elucidated the properties of smooth faults(1-3), but seem insufficient to explain the observed complexity of real fault dynamics(4,5). The recognition of a connection between fault-related processes and critical phenomena in other physical systems, together with numerical models of repeated earthquakes, have resulted in significant progress in the theoretical interpretation of earthquake scaling(4-14). But fault rheology and heterogeneity have so far been treated separately. Here I attempt to unify the requirements of fault rheology and heterogeneity using numerical calculations of quantized slip in an elastic continuum, I show that cyclical fault strength evolves naturally by means of a statistical selection for high-strength fault patches (asperities), resulting in the accumulation and eventual failure of those asperities, The applicability of these results to real fault systems is supported by a recent analysis of time-dependent earthquake statistics(15). These results imply that self-similarity and criticality on a fault emerge during an earthquake cycle, and suggest that the character of local seismicity can be useful in earthquake forecasting by revealing how advanced a fault is within its cycle.