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Introducing the activity parameter for elementary cellular automata

Author

Listed:
  • 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)

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.

Suggested Citation

  • Pablo Concha-Vega & Eric Goles & Pedro Montealegre & Martín Ríos-Wilson & Julio Santivañez, 2022. "Introducing the activity parameter for elementary cellular automata," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(09), pages 1-16, September.
    • Handle: RePEc:wsi:ijmpcx:v:33:y:2022:i:09:n:s0129183122501212
    DOI: 10.1142/S0129183122501212
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