A physics-based earthquake simulator should reproduce first-order empirical power-law behaviors of magnitudes and clustering. However, sequences exhibiting these laws have only been produced in discrete and low-dimension continuum simulations. We show that the same emergence also occurs in 3-D continuum simulations. Our model approximates a strike-slip fault system slipping under rate-and-state friction. We produce spatiotemporally clustered earthquake sequences exhibiting characteristic Gutenberg-Richter scaling as well as empirical inter-event time distribution. With fault interaction, partial ruptures emerge when seismogenic width W over characteristic nucleation length L_∞ is larger than 16.24, but none occurs without fault interaction. The mainshock recurrence times of individual faults remain quasi-periodic and fit a Brownian passage time distribution. The system mainshock recurrence time has a short-term Omori-type decay, indicating a 22% chance of mainshock clustering. These results show that physics-based multi-cycle models adequately reflect observed statistical signatures and show practical potential for long-term hazard assessment and medium-term forecasting.