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Simple rules, when executed by individual agents in a large group, or swarm, can lead to complex behaviors that are often difficult or impossible to predict knowing only the rules. However, aggregate behavior is not always unpredictable-even for swarm models said to be beyond analysis. For the class of swarming algorithms examined herein, we analytically identify several possible emergent behaviors and their underlying causes: clustering, drifting, and explosion. They also analyze the likelihood of these behaviors emerging from randomly selected swarm configurations and present a few examples. The analytic results are illustrated via simulation.
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