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I review the concept of self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales. Several exact results are demonstrated for the Abelian sandpile. Self-organized criticality concerns a class of dynamical systems which naturally drive themselves to a state where interesting physics occurs on all scales 1. The idea provides a possible " explanation " of the omnipresent multi-scale structures throughout the natural world, ranging from the fractal structure of mountains, to the power law spectra of earthquake sizes 2. Recent applications include such diverse topics as evolution 3 and traffic flow 4. The concept has even been invoked to explain the unpredictable nature of economic systems, i.e. why you can't beat the stock market 5. The prototypical example is a sandpile. On slowly adding grains of sand to an empty table, a pile will grow until its slope becomes critical and avalanches spill over the sides. If the slope becomes too large, a large catastrophic avalanche is likely, and the slope will reduce. If the slope is too small, then the sand will accumulate to make the pile steeper. Ultimately one should obtain avalanches of all sizes, with the prediction for the next being impossible without actually running the experiment. Self-organized criticality nicely compliments the concept of chaos. In the latter, dynamical systems with a few degrees of freedom, say three or more, can display highly complex behavior, including fractal structures. With self-organized criticality, we start instead with systems of many degrees of freedom, and find a few general common features. Another attraction of this topic is the ease with which computer models can be implemented and the elegance of the resulting graphics 6. The original Bak, Tang, Wiesenfeld paper 1 presented a simple model wherein each site in a two dimensional lattice has a state specified by a positive integer z i. This can be thought of as the amount of sand at that location, or, in another sense, as the slope of the sandpile at that point. Neither of these analogies is fully accurate, for the model has aspects of each. The dynamics follows by setting a threshold z T above which any given z i is unstable. Without loss of generality, I take this threshold to be z T = 3. Time now proceeds in discrete steps. In one such step …