Introducing the activity parameter for elementary cellular automata
Concha-Vega
P
author
Goles
E
author
Montealegre
P
author
Rios-Wilson
M
author
Santivanez
J
author
2022
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 R-1 is called a sub-rule of R-2 if the set of active transitions of R-1 is a subset of the active transitions of R-2.
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.
Discrete dynamical systems
elementary cellular automata
rule space
WOS:000840726100005
exported from refbase (show.php?record=1630), last updated on Mon, 12 Sep 2022 15:00:40 -0300
text
10.1142/S0129183122501212
Concha-Vega_etal2022
International Journal Of Modern Physics C
Int. J. Mod Phys. C
2022
continuing
periodical
academic journal
33
09
2250121
0129-1831