Natural algorithms We provide further evidence that the study of complex selforganizing 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 toweroftwos of height linear in the number of birds. We prove that, surprisingly, the toweroftwos 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.

Evolving Structures in Complex Systems In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This includes approaches based on compression algorithms and artificial neural networks. We believe such a metric can be useful for designing systems that could exhibit openended evolution, which itself might be a prerequisite for development of general artificial intelligence. We conduct experiments on 1D and 2D grid worlds and demonstrate that using the proposed metric we can automatically construct computational models with emerging properties similar to those found in the Conwayu0027s Game of Life, as well as many other emergent phenomena. Interestingly, some of the patterns we observe resemble forms of artificial life. Our metric of structural complexity growth can be applied to a wide range of complex systems, as it is not limited to cellular automata.