In this paper, we study different notions of stability for sand automata, dynamical systems inspired by sandpile models and cellular automata. First, we study the topological stability properties of equicontinuity and ultimate periodicity, proving that they are equivalent. Then, we deal with nilpotency. The classical definition for cellular automata being meaningless in that setting, we define a more suitable one. Finally, we prove that this dynamical behavior is undecidable.
Dennunzio, A., Guillon, P., Masson, B. (2008). Stable dynamics of sand automata. In Fifth IFIP International Conference on Theoretical Computer Science IFIP - TCS 2008 (pp.157-169). Springer [10.1007/978-0-387-09680-3].
Stable dynamics of sand automata
Dennunzio, A;
2008
Abstract
In this paper, we study different notions of stability for sand automata, dynamical systems inspired by sandpile models and cellular automata. First, we study the topological stability properties of equicontinuity and ultimate periodicity, proving that they are equivalent. Then, we deal with nilpotency. The classical definition for cellular automata being meaningless in that setting, we define a more suitable one. Finally, we prove that this dynamical behavior is undecidable.
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