AbstractCellular automata have proven effective in obtaining statistical insights into expected time series, magnitude‐frequency distributions, and average slip histories of earthquakes by confirming, for instance, the Gutenberg‐Richter magnitude‐frequency distribution and the existence of scaling functions for slip histories. Yet, exhaustive modeling is often required to obtain such insights since the model behavior is generally difficult to predict from fixed input parameters, such as the dissipation and long‐range stress interaction distance. We demonstrate that the temporal dynamics of a cellular automaton (CA), representing discretized equations of motion, can be simplified and modeled as an absorbing Markov chain with transition matrices that are fully determined by CA parameters. Time series, frequency‐size distributions, and slip histories of the Markov chain Monte Carlo (MCMC) and CA models are stochastically equivalent. The proposed method is a mean‐field approximation that replicates temporal CA statistics by ignoring spatial components. Fundamentally, the temporal portion of CA can be represented as a memoryless process in which the current outcome only depends on the immediate past. We believe the transparency of the statistical model may provide pertinent insights into the mean‐field behavior of a variety of physical applications near a critical state, including earthquake and avalanche patterns. For instance, the average slip histories display a typical but asymmetric shape due to a preferred path through probability space with initial acceleration of slip rate to peak size followed by slower deceleration toward rupture arrest.