Abstract
In this paper we introduce sand automata in order to give a common and useful framework for the study of most of the models of sandpiles. Moreover we give the possibility to have sources and sinks of “sand grains”. We prove a result which shows that the class of sand automata is rich enough to simulate any reasonable model of sandpiles based on local interaction rules. We also give an algorithm to find the fixed points of the evolutions of the sandpiles. Finally we prove that reversibility is equivalent to bijectivity.
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References
R. Anderson, L. Lovász, P. Shor, J. Spencer, E. Tardos, and S. Winograd. Disks, balls and walls: analysis of a combinatorial game. American mathematical monthly, 96:481–493, 1989.
P. Bak. How nature works-The science of SOC. Oxford University Press, 1997.
A. Bjorner and L. Lovász. Chip firing games on directed graphs. Journal of algebraic combinatorics, 1:305–328, 1992.
T. Brylawski. The lattice of integer partitions. Discrete mathematics, 6:201–219, 1973.
B. Durand. Global properties of cellular automata. In E. Goles and S. Martinez, editors, Cellular Automata and Complex Systems. Kluwer, 1998.
J. Durand-Lose. Automates cellulaires, automates à partition et tas de sable. PhD thesis, Université de Bordeaux-LABRI, 1996.
E. Goles. Sand pile automata. Annales Insitut Henri Poincaré, Physique Théorique, 56(1):75–90, 1992.
E. Goles and M. A. Kiwi. Game on line graphs and sandpile automata. Theoretical computer science, 115:321–349, 1993.
E. Goles and M. A. Kiwi. Sandpiles dynamics in a one-dimensional bounded lattice. Theoretical computer science, 136(2):527–532, 1994.
E. Goles, M. Morvan, and H. D. Phan. Lattice structure and convergence of a game of cards. Annals of Combinatorics, 2002. To appear.
E. Goles, M. Morvan, and H. D. Phan. Sandpiles and order structure of integer partitions. Discrete Applied Mathematics, 117(1–3):51–64, 2002.
E. Goles, M. Morvan, and H. D. Phan. The structure of linear chip firing game and related models. Theoretical Computer Science, 270:827–841, 2002.
H. J. Jensen. Self-organized criticality. Cambridge University Press, 1998.
H. D. Phan. Structures ordonnées et dynamique de pile de sable. PhD thesis, Université Denis Diderot Paris VII-LIAFA, 1999.
S. Wolfram. Theory and application of cellular automata. Wold Scientific Publishing Co., 1986.
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© 2003 Springer-Verlag Berlin Heidelberg
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Cervelle, J., Formenti, E. (2003). On Sand Automata. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_56
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DOI: https://doi.org/10.1007/3-540-36494-3_56
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Online ISBN: 978-3-540-36494-8
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