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Emergence of Distinct Spatial Patterns in Cellular Automata with Inertia: A Phase Transition-Like Behavior

K. Kramer,M. Koehler,C. E. Fiore,M. G. E. Luz

Published 2017 in Entropy

ABSTRACT

We propose a Cellular Automata (CA) model in which three ubiquitous and relevant processes in nature are present, namely, spatial competition, distinction between dynamically stronger and weaker agents and the existence of an inner resistance to changes in the actual state S n (=−1,0,+1) of each CA lattice cell n (which we call inertia). Considering ensembles of initial lattices, we study the average properties of the CA final stationary configuration structures resulting from the system time evolution. Assuming the inertia a (proper) control parameter, we identify qualitative changes in the CA spatial patterns resembling usual phase transitions. Interestingly, some of the observed features may be associated with continuous transitions (critical phenomena). However, certain quantities seem to present jumps, typical of discontinuous transitions. We argue that these apparent contradictory findings can be attributed to the inertia parameter’s discrete character. Along the work, we also briefly discuss a few potential applications for the present CA formulation.

PUBLICATION RECORD

  • Publication year

    2017

  • Venue

    Entropy

  • Publication date

    2017-03-07

  • Fields of study

    Mathematics, Physics, Computer Science

  • Identifiers
    DOI 10.3390/e19030102
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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