Natural algorithms

We provide further evidence that the study of complex self-organizing systems can benefit from an algorithmic perspective. The subject has been traditionally viewed through the lens of physics and control theory. Using tools typically associated with theoretical computer science, we settle an old question in theoretical ecology: bounding the convergence of bird flocks. We bound the time to reach steady state by a tower-of-twos of height linear in the number of birds. We prove that, surprisingly, the tower-of-twos growth is intrinsic to the model. This unexpected result demonstrates the merits of approaching biological dynamical systems as "natural algorithms" and applying algorithmic techniques to them.