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Theses

Systèmes de particules et collisions discrètes dans les automates cellulaires

Abstract : The main goal of this thesis is to study systems of particles and collisions in cellular automata. Starting from experimental observations, we give formal definitions of these objects and show how they relate to regular colorings of the plane. Using a symbolic representation of those objects, we introduce a syntactical operation on them: catenation schemes. This operation is linked to an informal operation usually used in algorithmics on cellular automata through a coloring interpretation. We show that, in the case of finite catenation schemes, this link can be completely characterised in an algorithmic way. Then we explore possibilities of extensions of this result to ease encoding or overcome the finite limitation. At last, we study applications of these systems to study universality in cellular automata. In particular, we give a new proof of universality of rule 110 and give the construction of an intrinsically universal cellular automaton with radius 1 and only 4 states.
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https://tel.archives-ouvertes.fr/tel-00347778
Contributor : Gaétan Richard <>
Submitted on : Tuesday, December 16, 2008 - 4:48:00 PM
Last modification on : Thursday, April 25, 2019 - 11:26:04 AM
Long-term archiving on: : Thursday, October 11, 2012 - 1:55:43 PM

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Gaétan Richard. Systèmes de particules et collisions discrètes dans les automates cellulaires. Autre [cs.OH]. Université de Provence - Aix-Marseille I, 2008. Français. ⟨tel-00347778⟩

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