Abstract
Standard Cellular Automata (CA) are memoryless: i.e., the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article considers an extension to the standard framework of CA by implementing memory capabilities in cells. Thus in CA with memory : while the update rules remain unaltered, historic memory of past iterations is retained by featuring each cell by a summary of all its past states. A study is made of the effect of historic memory on two given sides of the hypercube of elementary probabilistic CA.
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References
Ilachinski, A.: Cellular Automata. A Discrete Universe. World Scientific, Singapore (2000)
Alonso-Sanz, R.: One-dimensional, r=2 cellular automata with memory. Int. J. Bifurcation and Chaos 14 (in press)
Alonso-Sanz, R., Martin, M.: Three-state one-dimensional cellular automata with memory. Chaos, Solitons and Fractals 21, 809–834 (2004)
Alonso-Sanz, R.: Reversible CA with Memory. Physica D 175, 1–30 (2003)
Alonso-Sanz, R., Martin, M.: Elementary cellular automata with memory. Complex Systems 14, 99–126 (2003)
Alonso-Sanz, R., Martin, M.: Cellular automata with accumulative memory. Int. J. Modern Physics C 14, 695–719 (2003)
Alonso-Sanz, R., Martin, M.C., Martin, M.: One-dimensional cellular automata with memory. Int. J. Bifurcation and Chaos 12, 205–226 (2002)
Alonso-Sanz, R., Martin, M.C., Martin, M.: Two-dimensional cellular automata with memory. Int. J. Modern Physics C 13, 49–65 (2002); and the references therein
Adamatzky, A.: Identification of Cellular Automata. Taylor & Francis, Abington (1994)
Kinzel, W.: Phase Transitions of CA. Z. für Physics B 58, 229–244 (1985)
Domany, E., Kinzel, W.: Equivalence of Cellular Automata to Ising Models and Directed Percolation. Physical Review Letters 53, 311–314 (1984)
Lebowitz, J.L., Maes, C., Speer, E.: Statistical Methods of Probabilistic Cellular Automata. J. Statistical Physics 59, 117–170 (1990)
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Alonso-Sanz, R., Martín, M. (2004). Elementary Probabilistic Cellular Automata with Memory in Cells. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30479-1_2
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DOI: https://doi.org/10.1007/978-3-540-30479-1_2
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