On the dynamics of cellular automata with memory

Mart�nez, Genaro J.; Adamatzky, Andrew; Alonso-Sanz, Ramon

Abstract

Elementary cellular automata (ECA) are linear arrays of finite-state machines (cells) which take binary states, and update their states simultaneously depending on states of their closest neighbours. We design and study ECA with memory (ECAM), where every cell remembers its states during some fixed period of evolution. We characterize complexity of ECAM in a case study of rule 126, and then provide detailed behavioural classification of ECAM. We show that by enriching ECA with memory we can achieve transitions between the classes of behavioural complexity. We also show that memory helps to 'discover' hidden information and behaviour on trivial (uniform, periodic), and non-trivial (chaotic, complex) dynamical systems.

• Journal Article Type: Article
• Acceptance Date: Jan 1, 2015
• Online Publication Date: Jan 1, 2015
• Publication Date: Jan 1, 2015
• Journal: Fundamenta Informaticae
• Electronic ISSN: 0169-2968
• Publisher: IOS Press
• Peer Reviewed: Peer Reviewed
• Volume: 138
• Issue: 1-2
• Pages: 1-16
• DOI: https://doi.org/10.3233/FI-2015-1194
• Keywords: uniform, periodic, non-trivial chaotic, complex dynamical systems, elementary cellular automata, classification, memory, computability, gliders, collisions, complex systems
• Public URL: https://uwe-repository.worktribe.com/output/843216
• Publisher URL: http://dx.doi.org/10.3233/FI-2015-1194