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Homogeneous Dynamics for Square Boolean Automata with Null Boundary Conditions

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Computational Science and Its Applications – ICCSA 2014 (ICCSA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8579))

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Abstract

This paper is concerned with the study of square Boolean four-neighbor peripheral cellular automata with boundary conditions fixed as zero. It is first shown that, due to plane reflection symmetry transformations, the number of dynamically nonequivalent such automata is equal to 9 616. The dynamics of the two homogeneous configurations are studied and it is shown that, in contrast with what happens in the case of periodic boundary conditions, the homogeneous configuration consisting only of ones can have various interesting dynamics, including the one typically observed for automata in Wolfram’s Class III. Finally, an example of a rule where there is coexistence between a homogeneous final state and other dynamics is presented.

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Author information

Authors and Affiliations

  1. Departamento de Matemática e Aplicações, Universidade do Minho, Portugal

    Ricardo Severino

  2. Departamento de Matemática e Aplicações and NIPE, Universidade do Minho, Portugal

    Maria Joana Soares

  3. Departamento de Matemática e Aplicações and CMAT, Universidade do Minho, Portugal

    Maria Emilia Athayde

Authors
  1. Ricardo Severino
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  2. Maria Joana Soares
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  3. Maria Emilia Athayde
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Editor information

Editors and Affiliations

  1. School of Engineering, University of Basilicata, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Computer and Information Sciences, Covenant University, Ota, Nigeria

    Sanjay Misra

  3. Department of Production and Systems, University of Minho, 4710-057, Braga, Portugal

    Ana Maria A. C. Rocha

  4. DICAR, Polytecnico di Bari, 70125, Bari, Italy

    Carmelo Torre

  5. University of Minho, Braga, Portugal

    Jorge Gustavo Rocha  & Maria Irene Falcão  & 

  6. Monash University, 3800, Clayton, VIC, Australia

    David Taniar

  7. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, 813-8503, Higashi-ku, Fukuoka, Japan

    Bernady O. Apduhan

  8. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

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Severino, R., Soares, M.J., Athayde, M.E. (2014). Homogeneous Dynamics for Square Boolean Automata with Null Boundary Conditions. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8579. Springer, Cham. https://doi.org/10.1007/978-3-319-09144-0_3

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  • DOI: https://doi.org/10.1007/978-3-319-09144-0_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09143-3

  • Online ISBN: 978-3-319-09144-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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