Introducing the activity parameter for elementary cellular automata

Pablo Concha-Vega (), Eric Goles (), Pedro Montealegre, Martín Ríos-Wilson () and Julio Santivañez ()
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Pablo Concha-Vega: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avenida Diagonal Las Torres 2640, Peñalolén, Santiago de Chile, Chile
Eric Goles: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avenida Diagonal Las Torres 2640, Peñalolén, Santiago de Chile, Chile
Pedro Montealegre: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avenida Diagonal Las Torres 2640, Peñalolén, Santiago de Chile, Chile
Martín Ríos-Wilson: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avenida Diagonal Las Torres 2640, Peñalolén, Santiago de Chile, Chile
Julio Santivañez: Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avenida Diagonal Las Torres 2640, Peñalolén, Santiago de Chile, Chile

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 09, 1-16

Abstract: Given an elementary cellular automaton (ECA) with local transition rule R, two different types of local transitions are identified: the ones in which a cell remains in its current state, called inactive transitions, and the ones in which the cell changes its current state, which are called active transitions. The number of active transitions of a rule is called its activity value. Based on latter identification, a rule R1 is called a sub-rule of R2 if the set of active transitions of R1 is a subset of the active transitions of R2.In this paper, the notion of sub-rule for elementary cellular automata is introduced and explored: first, we consider a lattice that illustrates relations of nonequivalent elementary cellular automata according to nearby sub-rules. Then, we introduce statistical measures that allow us to compare rules and sub-rules. Finally, we explore the possible similarities in the dynamics of a rule with respect to its sub-rules, obtaining both empirical and theoretical results.

Keywords: Discrete dynamical systems; elementary cellular automata; rule space (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122501212

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