On the set of Fixed Points of the Parallel Symmetric Sand Pile Model

2 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
3 MC2 - Modèles de calcul, Complexité, Combinatoire
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of $\textit{Self-Organized Criticality}$. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Using a comparison with the Symmetric Sand Pile Model (SSPM) on which rules are applied once at each iteration, we get a continuity property. This property states that within PSSPM we can't reach every fixed points of SSPM, but a continuous subset according to the lexicographic order. Moreover we define a successor relation to browse exhaustively the sets of fixed points of those models.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [15 references]

https://hal.inria.fr/hal-01196141
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Wednesday, September 9, 2015 - 11:15:01 AM
Last modification on : Saturday, September 11, 2021 - 3:17:40 AM
Long-term archiving on: : Monday, December 28, 2015 - 11:09:18 PM

File

dmAP0102.pdf
Publisher files allowed on an open archive

Identifiers

• HAL Id : hal-01196141, version 1

Citation

Kévin Perrot, Thi Ha Duong Phan, Trung Van Pham. On the set of Fixed Points of the Parallel Symmetric Sand Pile Model. AUTOMATA 2011, Nov 2011, Santiago, Chile. pp.17-28. ⟨hal-01196141⟩

Record views