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Effects of a Vanishing Noise on Elementary Cellular Automata Phase-Space Structure

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Cellular Automata (ACRI 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14978))

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Abstract

We investigate elementary cellular automata from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal elementary cellular automata, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is that this modification not always goes in the sense of decreasing the entropy.

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Acknowledgments

This publication was produced with the co-funding of European Union - Next Generation EU, in the context of The National Recovery and Resilience Plan, Investment 1.5 Ecosystems of Innovation, Project Tuscany Health Ecosystem (THE), CUP: B83C22003920001.

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Authors and Affiliations

  1. Department of Physics and Astronomy and CSDC, University of Florence, via G. Sansone 1, 50019, Sesto Fiorentino, Italy

    Franco Bagnoli, Michele Baia & Tommaso Matteuzzi

  2. INFN, Florence sect., Florence, Italy

    Franco Bagnoli & Michele Baia

  3. UMR Espace-Dev, University of Perpignan, via Domitia, Perpignan, France

    Franco Bagnoli

Authors
  1. Franco Bagnoli
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  2. Michele Baia
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  3. Tommaso Matteuzzi
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Corresponding author

Correspondence to Franco Bagnoli .

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Editors and Affiliations

  1. University of Florence, Sesto Fiorentino, Italy

    Franco Bagnoli

  2. Ghent University, Ghent, Belgium

    Jan Baetens

  3. University of Milano-Bicocca, Milan, Italy

    Stefania Bandini

  4. University of Florence, Sesto Fiorentino, Italy

    Tommaso Matteuzzi

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Bagnoli, F., Baia, M., Matteuzzi, T. (2024). Effects of a Vanishing Noise on Elementary Cellular Automata Phase-Space Structure. In: Bagnoli, F., Baetens, J., Bandini, S., Matteuzzi, T. (eds) Cellular Automata. ACRI 2024. Lecture Notes in Computer Science, vol 14978. Springer, Cham. https://doi.org/10.1007/978-3-031-71552-5_5

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  • DOI: https://doi.org/10.1007/978-3-031-71552-5_5

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-71552-5

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