TY - JOUR

T1 - Introducing the activity parameter for elementary cellular automata

AU - Concha-Vega, Pablo

AU - Goles, Eric

AU - Montealegre, Pedro

AU - Ríos-Wilson, Martín

AU - Santivañez, Julio

N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - 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.

AB - 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.

KW - Discrete dynamical systems

KW - elementary cellular automata

KW - rule space

UR - http://www.scopus.com/inward/record.url?scp=85127085724&partnerID=8YFLogxK

U2 - 10.1142/S0129183122501212

DO - 10.1142/S0129183122501212

M3 - Article

AN - SCOPUS:85127085724

SN - 0129-1831

VL - 33

JO - International Journal of Modern Physics C

JF - International Journal of Modern Physics C

IS - 9

M1 - 2250121

ER -