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A Survey on the Stability of (Extended) Linear Sand Pile Model

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Part of the Emergence, Complexity and Computation book series (ECC,volume 42)

Abstract

We give a survey of our works on the natural extensions of the well-known Sand Pile Model. These extensions consist of adding outside grains on random columns, allowing sand grains to move from left to right and from right to left, considering cycle graphs and the extension to infinity. We study the reachable configurations and fixed points of each model and show how to compute the set of fixed points, the time of convergence and the distribution of fixed points.

dedicated to the 70th Anniversary of Eric Goles.

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Acknowledgements

This work was supported by the Vietnam National Foundation for Science ans Technology Development under the grant number NAFOSTED 101.99-2016.16 and by the Vietnam Institute for Advanced Study in Mathematics.

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Correspondence to Thi Ha Duong Phan .

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Phan, T.H.D. (2022). A Survey on the Stability of (Extended) Linear Sand Pile Model. In: Adamatzky, A. (eds) Automata and Complexity. Emergence, Complexity and Computation, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-92551-2_16

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  • DOI: https://doi.org/10.1007/978-3-030-92551-2_16

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