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Des piles de sable aux automates de sable

Abstract : In this thesis we study several discrete dynamical systems which can simulate the formation of sandpiles. The behavior of the basic models SPM and IPM(k) is well-known under specific initial conditions. We extend these results to arbitrary initial conditions. Moreover, we introduce the model SSPM which adds symmetry to these models and improves their realism. In the second part, we study another dynamical system, namely sand automata. They are defined similarly to cellular automata, with the constraint that configurations can not contain any "hole˝. These automata can simulate any locally-defined sandpile model, and their solid topological framework allows more general results. We are interested in sand automata dynamics, more precisely in the reversibility properties of sand automata. We conclude by studying the decidability of properties which characterize classical sandpile systems: grain conservation and ultimate periodicity.
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https://tel.archives-ouvertes.fr/tel-00144448
Contributor : Benoît Masson <>
Submitted on : Thursday, May 3, 2007 - 1:58:55 PM
Last modification on : Monday, October 12, 2020 - 10:30:28 AM
Long-term archiving on: : Wednesday, April 7, 2010 - 2:12:39 AM

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Benoît Masson. Des piles de sable aux automates de sable. Modélisation et simulation. Université Nice Sophia Antipolis, 2006. Français. ⟨tel-00144448⟩

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