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A discrete model is set up using the cellular automaton method and applied to simulate the formation and evolution of aeolian bedforms. The calculated bedforms resemble the actual shape of natural sand ripples and dunes.This reveals that the sand movement is a typical nonlinear dynamical process, and that the nesting configuration of sand ripples, dunes and draas are a self-organized system with a fractal characteristic, and evotves simultaneously at various scales in the sand-airflow.