Emergence of Distinct Spatial Patterns in Cellular Automata with Inertia: A Phase Transition-Like Behavior
CEPLAN, Universidade do Estado de Santa Catarina, 89283-081 São Bento do Sul-SC, Brazil
Departamento de Física, Universidade Federal do Paraná, C.P. 19044, 81531-980 Curitiba-PR, Brazil
Instituto de Física, Universidade de São Paulo, C.P. 66318, 05315-970 São Paulo-SP, Brazil
Author to whom correspondence should be addressed.
Academic Editor: Mikhail Prokopenko
Received: 24 December 2016 / Revised: 20 February 2017 / Accepted: 28 February 2017 / Published: 7 March 2017
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
(=−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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Kramer, K.; Koehler, M.; Fiore, C.E.; da Luz, M.G. Emergence of Distinct Spatial Patterns in Cellular Automata with Inertia: A Phase Transition-Like Behavior. Entropy 2017, 19, 102.
Kramer K, Koehler M, Fiore CE, da Luz MG. Emergence of Distinct Spatial Patterns in Cellular Automata with Inertia: A Phase Transition-Like Behavior. Entropy. 2017; 19(3):102.
Kramer, Klaus; Koehler, Marlus; Fiore, Carlos E.; da Luz, Marcos G. 2017. "Emergence of Distinct Spatial Patterns in Cellular Automata with Inertia: A Phase Transition-Like Behavior." Entropy 19, no. 3: 102.
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