We developed a cellular automata model of fluid circulation within a rock matrix to test whether considering a volcano as a complex system helps understand the observed eruptive and seismicity patterns of the Piton de la Fournaise (PF) volcano. In this model, fluid and rock cells interact through locally defined rules, including a steady increase of pressure, a threshold dynamics, a fluid redistribution algorithm, and an energy dissipation process. Comparison of the model results and observations for more than 40 simulations provides information on the mechanics of the PF volcano and basaltic volcanoes in general. First, we demonstrate that the multiple lenses magma storage model for the summit reservoir of basaltic volcanoes is consistent with the PF 1920--1992 eruptive pattern, proposing an alternative to the macrochamber model. Second, we show that the great number of interactions between magma storage lenses in a critical state may work as a nonlinear filter, modifying a possible uniform increase of pressure in the input, induced by deep magma supply and gas exsolution during crystallization, into a nonlinear fluid flow emergence in time and size, both unpredictable and organized in nonrandom scaling statistics. The fluid-rock cellular automaton allows us to explore scales ranging from global Earth mantle to porous rock matrix, thus rationalizing the power law volume distribution of total eruptions on the Earth surface <Mc Clelland et al., 1989> and the hierarchical organization that is reported for many types of fluid-induced seismicity <Grasso, 1993; Miller et al., 1996>, respectively. ¿ 1998 American Geophysical Union