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      Deterministic phase transitions and self-organization in logistic cellular automata

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      Author
      İbrahimi, Muhamet
      Gülseren, Oğuz
      Jahangirov, Seymur
      Date
      2019
      Source Title
      Physical Review E
      Print ISSN
      2470-0045
      Publisher
      American Physical Society
      Volume
      100
      Issue
      4
      Pages
      042216-1 - 042216-9
      Language
      English
      Type
      Article
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      Abstract
      We present a simple extension in which a single parameter tunes the dynamics of cellular automata (CA) by consequently expanding their discrete state space into a Cantor set. Such an implementation serves as a potent platform for further investigation of several emergent phenomena, including deterministic phase transitions, pattern formation, autocatalysis, and self-organization. We first apply this approach to Conway's Game of Life and observe sudden changes in the asymptotic dynamics of the system accompanied by the emergence of complex propagators. Incorporation of the new state space with system features is used to explain the transitions and formulate the tuning parameter range where the propagators adaptively survive by investigating their autocatalytic local interactions. Similar behavior is present when the same recipe is applied to Rule 90, an outer totalistic elementary one-dimensional cellular automaton. In addition, the latter case shows that deterministic transitions between classes of CA can be achieved by tuning a single parameter continuously.
      Keywords
      Chaos
      Complex systems
      Emergence of patterns
      Phase transitions
      Permalink
      http://hdl.handle.net/11693/53254
      Published Version (Please cite this version)
      https://dx.doi.org/10.1103/PhysRevE.100.042216
      Collections
      • Aysel Sabuncu Brain Research Center (BAM) 183
      • Department of Physics 2299
      • Institute of Materials Science and Nanotechnology (UNAM) 1775
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