episciences.org_2974_20230328191233040
20230328191233040
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
01
01
2011
DMTCS Proceedings vol. AP,...
Proceedings
On the set of Fixed Points of the Parallel Symmetric Sand Pile Model
Kévin
Perrot
Thi Ha Duong
Phan
Trung Van
Pham
Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of $\textit{SelfOrganized Criticality}$. 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.
01
01
2011
2974
https://hal.science/hal01196141v1
10.46298/dmtcs.2974
https://dmtcs.episciences.org/2974

https://dmtcs.episciences.org/2974/pdf

https://dmtcs.episciences.org/2974/pdf