Balancing vectors in the max norm
Combinatorica
Disks, balls, and walls: analysis of a combinatorial game
American Mathematical Monthly
Games on line graphs and sand piles
Theoretical Computer Science
Chaotic subshifts and related languages applications to one-dimensional cellular automata
Fundamenta Informaticae - Special issue on cellular automata
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Consistency of the Adiabatic Theorem
Quantum Information Processing
Solution of some conjectures about topological properties of linear cellular automata
Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
Entropies and Co-Entropies of Coverings with Application to Incomplete Information Systems
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Advances in Symmetric Sandpiles
Fundamenta Informaticae
Fundamental study: From sandpiles to sand automata
Theoretical Computer Science
A Predator-Prey Cellular Automaton with Parasitic Interactions and Environmental Effects
Fundamenta Informaticae
Conservation of some dynamical properties for operations on cellular automata
Theoretical Computer Science
Sand automata as cellular automata
Theoretical Computer Science
Information Entropy and Granulation Co---Entropy of Partitions and Coverings: A Summary
Transactions on Rough Sets X
On the directional dynamics of additive cellular automata
Theoretical Computer Science
Entropies and co-entropies for incomplete information systems
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
Basic properties for sand automata
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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We analyze the dynamical behavior of the usual one dimensional sand pile model which actually describes the physical situation in which the pile is submitted to the uniform blow of a unidirectional wind. In the first step the Lagrangian formalism is investigated, showing that the stationary action principle does not select in a unique way the path which satisfies either the minimal or the maximal action principle. This drawback is solved making use of the information (Shannon) entropy which enables one to determine the unique path in which at any time step the entropy variation is minimal (adiabatic) or maximal (anti-adiabatic). A cellular automata (CA) model describing this sand pile behavior is introduced, and the consequent deterministic dynamic is compared with the entropy results, showing that also in this case there are some drawbacks. Moreover, it is shown that our CA local rule is a particular case of some standard CA sand pile models present in literature.