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Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…

High Energy Physics - Lattice · Physics 2008-02-03 Michael Creutz

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata…

Computational Complexity · Computer Science 2008-12-18 Alberto Dennunzio , Pierre Guillon , Benoît Masson

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

Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…

Logic in Computer Science · Computer Science 2015-04-14 Nachum Dershowitz , Evgenia Falkovich

Three reasonable hypotheses lead to the thesis that physical phenomena can be described and simulated with cellular automata. In this work, we attempt to describe the motion of a particle upon which a constant force is applied, with a…

Cellular Automata and Lattice Gases · Physics 2016-03-09 Pablo Arrighi , Gilles Dowek

Classical reversible cellular automata (CAs), which describe the discrete-time dynamics of classical degrees of freedom in a finite state-space, can exhibit exact, nonthermal quantum eigenstates despite being classically chaotic. We show…

Strongly Correlated Electrons · Physics 2020-11-30 Thomas Iadecola , Sagar Vijay

One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…

Cellular Automata and Lattice Gases · Physics 2025-12-10 Martin Schaller , Karl Svozil

Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…

Discrete Mathematics · Computer Science 2008-09-11 Donny Cheung , Carlos A. Perez-Delgado

The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…

Cellular Automata and Lattice Gases · Physics 2009-02-03 Franco Bagnoli , Raul Rechtman

Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…

Statistical Mechanics · Physics 2021-07-07 Marco Baldovin , Stefano Iubini , Roberto Livi , Angelo Vulpiani

The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…

Quantum Physics · Physics 2021-07-09 Paolo Perinotti

This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…

Dynamical Systems · Mathematics 2018-06-05 Benjamin Hellouin de Menibus , Mathieu Sablik

Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…

Cellular Automata and Lattice Gases · Physics 2025-07-10 Michiel Rollier , Kallil M. C. Zielinski , Aisling J. Daly , Odemir M. Bruno , Jan M. Baetens

We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable injectivity, stable reversibility, stable post-surjectivity…

Dynamical Systems · Mathematics 2022-03-03 Xuan Kien Phung

We construct a one-dimensional uniquely ergodic cellular automaton which is not nilpotent. This automaton can perform asymptotically infinitely sparse computation, which nevertheless never disappears completely. The construction builds on…

Dynamical Systems · Mathematics 2014-08-29 Ilkka Törmä

A model for 1D traffic flow is developed, which is discrete in space and time. Like the cellular automaton model by Nagel and Schreckenberg [J. Phys. I France 2, 2221 (1992)], it is simple, fast, and can describe stop-and-go traffic. Due to…

Statistical Mechanics · Physics 2009-10-31 Dirk Helbing , Michael Schreckenberg

We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…

Cellular Automata and Lattice Gases · Physics 2012-03-29 Genaro J. Martinez , Andrew Adamatzky , Ramon Alonso-Sanz

Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…

Discrete Mathematics · Computer Science 2009-02-10 Laurent Boyer , Guillaume Theyssier

Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…

Statistical Mechanics · Physics 2016-07-06 Emilio N. M. Cirillo , Francesca R. Nardi , Cristian Spitoni

The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…

Computational Complexity · Computer Science 2009-06-22 Eric Goles , Pierre-Etienne Meunier , Ivan Rapaport , Guillaume Theyssier