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Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…

Dynamical Systems · Mathematics 2009-02-10 Pietro Di Lena , Luciano Margara

Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…

Statistical Mechanics · Physics 2026-03-31 Mihir Metkar , Neha Sah , Yichen Zhou

Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…

Dynamical Systems · Mathematics 2019-04-30 Rezki Chemlal

Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more…

Discrete Mathematics · Computer Science 2009-04-29 Mathieu Sablik , Guillaume Theyssier

To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…

Cellular Automata and Lattice Gases · Physics 2018-03-20 Yanbo Zhang

Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…

Cellular Automata and Lattice Gases · Physics 2024-10-30 Temitayo Adefemi

While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…

Cellular Automata and Lattice Gases · Physics 2019-04-15 E. Estevez-Rams , D. Estevez-Moya , K. Garcia-Medina , R. Lora-Serrano

Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Nazim A. Fates , Michel Morvan

Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…

Condensed Matter · Physics 2015-06-25 Avinash Dhar , Porus Lakdawala , Gautam Mandal , Spenta R. Wadia

Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Cosma Rohilla Shalizi , Kristina Lisa Shalizi

This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the…

Cellular Automata and Lattice Gases · Physics 2013-04-05 Genaro J. Martinez , Juan C. Seck-Tuoh-Mora , Hector Zenil

Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the…

Emerging Technologies · Computer Science 2022-11-04 Gordon H. Y. Li , Christian R. Leefmans , James Williams , Alireza Marandi

Elementary cellular automata (ECA) are one-dimensional discrete models of computation with a small memory set that have gained significant interest since the pioneer work of Stephen Wolfram, who studied them as time-discrete dynamical…

Cellular Automata and Lattice Gases · Physics 2025-08-12 Alonso Castillo-Ramirez , Maria G. Magaña-Chavez

Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…

Statistical Mechanics · Physics 2026-05-27 Rustem Sharipov , Matija Koterle , Sašo Grozdanov , Tomaž Prosen

Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into…

Cellular Automata and Lattice Gases · Physics 2024-06-10 Wout Merbis , Calvin Bakker

We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically…

Cellular Automata and Lattice Gases · Physics 2013-04-09 Markus Redeker , Andrew Adamatzky , Genaro J. Martínez

This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…

Computational Complexity · Computer Science 2007-05-23 Maxim Makatchev

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…

Formal Languages and Automata Theory · Computer Science 2024-01-17 Kamalika Bhattacharjee , Nazma Naskar , Souvik Roy , Sukanta Das

We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…

Cellular Automata and Lattice Gases · Physics 2007-05-23 Jean-Baptiste Rouquier , Michel Morvan

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in…