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Animal movement patterns have long been the subject of mathematical and ecological interest. How do individual behavioral decision rules translate into macroscale patterns of space use such as foraging, patrolling or , territories? A mixture of tools including mechanistic models, random walks and other mathematical tools can be used to connect underlying processes to the observed patterns. Here interactions are complex and may involve memory of past events, as well as a cognitive map. I will connect the models closely to detailed biological data, and make applications to a spectrum of different emerging patterns, ranging from territories in Amazonian birds to patrolling in wolves.