Diameter mean equicontinuity and cellular automata
Luguis de los Santos Ba\~nos, Felipe Garc\'ia-Ramos
TL;DR
This paper investigates the properties of diameter mean equicontinuity in cellular automata, demonstrating that the Pacman automaton lacks this property despite being almost mean equicontinuous, thus highlighting distinctions in dynamical behaviors.
Contribution
It introduces the concept of diameter mean equicontinuity in cellular automata and shows that the Pacman automaton does not possess this property, contrasting with its known mean equicontinuity.
Findings
Pacman automaton is not almost diam-mean equicontinuous
Pacman automaton is almost mean equicontinuous
Distinction between mean and diam-mean equicontinuity in cellular automata
Abstract
Mean and diam-mean equicontinuity are dynamical properties that have been of use in the study of non-periodic order. We show that the Pacman automaton is not almost diam-mean equicontinuous (it is already known that it is almost mean equicontinuous).
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Taxonomy
TopicsCellular Automata and Applications · Mathematical Dynamics and Fractals · Computability, Logic, AI Algorithms