Water is a key resource in determining the composition and structure of savanna ecosystems. In this study we present a simple cellular automata model in which death and reproduction chances of trees and grasses are based on the dynamical description of plant water stress by a probabilistic ecohydrological point model, using the parameterization for a Texas savanna. The results show that the model behavior, despite its simplicity, can be linked to ecological reality: the model yields a dynamic tree-grass coexistence driven by the annual rainfall, and the space-time behavior shows that both random and clustered tree distributions for periods up to 100 years can be observed. Both temporal and spatial model output display fractal characteristics suggesting the possibility of a self-organized critical dynamics. Thus power law behavior is observed in both the spectral density function and the cluster size distribution. The presence of spatial fractal characteristic opens avenues for more thorough model testing.