Self-organized growth model for the quenched Herring-Mullin equation

We introduce a simple self-organized growth model mimicking the dynamics of a driven tensionless interface in a random medium near the depinning threshold. The roughness and growth exponents for the model are obtained as zeta approximately 1.93 and beta approximately 0.96, respectively. We discuss the possible continuum equation describing the motion of a driven interface in our model.