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[en] The leader election problem is a crucial problem in the theory of distributed algorithms, multi-agent systems as well as in sociobiology. In this paper we investigate one-dimensional binary state cellular automata with an intention to track self-organizational mechanisms that finally enable a global leader to be elected. Since our model is anonymous and uniform we also have to deal with a problem of symmetry that in great majority of cases is broken by inhomogeneity of arbitrary initial configurations. Our approach to the problem is based on the evolution of cellular automata by genetic algorithms and the methodology of computational mechanics. The presented new solution of the leader election reaches remarkably high performance of 94 − 99%. The analysis shows a sophisticated collective computation demonstrated by so called particles and their interactions. Due to the simplicity of our model, presented approach is general and universal enough to be applicable even at the level of primitive biological or artificial societies.