Self-organization in cellular automata: a particle-based approach

Authors:
Benjamin Hellouin De Menibus;Mathieu Sablik
Affiliations:
Laboratoire d'Informatique Fondamentale, Université de Provence, Marseille, France;Laboratoire d'Informatique Fondamentale, Université de Provence, Marseille, France
Venue:
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Year:
2011

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Abstract

For some classes of cellular automata, we observe empirically a phenomenon of self-organization: starting from a random configuration, regular strips separated by defects appear in the space-time diagram. When there is no creation of defects, all defects have the same direction after some time. In this article, we propose to formalise this phenomenon. Starting from the notion of propagation of defect by a cellular automaton formalized in [Piv07b, Piv07a], we show that, when iterating the automaton on a random configuration, defects in one direction only remain asymptotically.