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We show that continuum driven dissipative systems can be driven to a state whose response to continuous energy input is to dissipate energy by a power law distribution of avalanches. We describe under what circumstances this type of behavior will occur, and how it can be modelled using very much simpler cellular automata. We show how this formalism can be applied to solar active regions, which gives a physical explanation of why our earlier cellular automaton models were able to so accurately reproduce the observed distributions of solar flares. We will also give some further applications of this approach.
