A model to simulate the time evolution of river delta formation process is presented. It is based on the continuity equation for water and sediment flow and a phenomenological sedimentation/ erosion law. Different delta types are reproduced by using different parameters and erosion rules. The structures of the calculated patterns are analyzed in space and time and compared with real data patterns. Furthermore, our model is capable of simulating the rich dynamics related to the switching of the mouth of the river delta. The simulation results are then compared with geological records for the Mississippi River. fractals ͉ lattice model T he texture of the landscape and fluvial basins is the product of thousands of years of tectonic movement coupled with erosion and weathering caused by water flow and climatic processes. To gain insight into the time evolution of the topography, a model has to include the essential processes responsible for the changes of the landscape. In geology, the formation of river deltas and braided river streams has long been studied, describing the schematic processes for the formation of deltaic distributaries and interlevee basins (1-5). Experimental investigation of erosion and deposition has a long tradition in geology (6). Field studies have been carried out for the Mississippi River delta (7-10), the Niger River delta (11-13), and the Brahmaputra River delta (14). Laboratory experiments have also been set up in the last decades for quantitative measurements (15)(16)(17)(18)(19). For instance, in the eXperimental EarthScape (XES) project, the formation of river deltas is studied on laboratory scale, and different measurements have been carried out (20)(21)(22).Nevertheless, modeling has proven to be very difficult because the system is highly complex and a large range of time scales is involved. To simulate geological time scales, the computation power is immense and classical hydrodynamical models cannot be applied. Typically, these models are based on a continuous ansatz (e.g., shallow water equations), which describes the interaction of the physical laws for erosion, deposition, and water flow (23-28). The resulting set of partial differential equations are then solved with boundary and initial conditions using classical finite element or finite volume schemes. Unfortunately, none of these continuum models is able to simulate realistic land forms because the computational effort is much too high to reproduce the necessary resolution over realistic time scales. Therefore, in recent years, discrete models based on the idea of cellular automata have been proposed (29-34). These models consider water input on some nodes of the lattice and look for the steepest path in the landscape to distribute the flow. The sediment flow is defined as a nonlinear function of the water flow, and the erosion and deposition are obtained by the difference of the sediment inflow and outflow. This process is iterated to obtain the time evolution. In contrast to the former models, these models are fast and ...