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On the dynamics of cellular automata with memory

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


Genaro J. Mart�nez

Ramon Alonso-Sanz


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.


Martínez, G. J., Adamatzky, A., & Alonso-Sanz, R. (2015). On the dynamics of cellular automata with memory. Fundamenta Informaticae, 138(1-2), 1-16.

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 1875-8681
Publisher IOS Press
Peer Reviewed Peer Reviewed
Volume 138
Issue 1-2
Pages 1-16
Keywords uniform, periodic, non-trivial chaotic, complex dynamical systems, elementary cellular automata, classification, memory, computability, gliders, collisions, complex systems
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