On the set of Fixed Points of the Parallel Symmetric Sand Pile Model - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2011

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

Résumé

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.
Fichier principal
Vignette du fichier
dmAP0102.pdf (302.53 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01196141 , version 1 (09-09-2015)

Identifiants

Citer

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, ⟨10.46298/dmtcs.2974⟩. ⟨hal-01196141⟩
234 Consultations
661 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More