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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 are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a…

Cellular Automata and Lattice Gases · Physics 2025-08-11 Genaro J. Martinez , Andrew Adamatzky , Guanrong Chen

The prediction of the behavior of the disease, the level of affectation in a population and the ways to control it are the most important aspects studied by epidemiology using tools such as historical data and mathematical models. So, our…

Dynamical Systems · Mathematics 2022-04-04 Jorge Andrés Ibáñez Huertas , Carlos Isaac Zainea Maya

This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…

Discrete Mathematics · Computer Science 2010-08-23 Martin Delacourt , Victor Poupet , Mathieu Sablik , Guillaume Theyssier

A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…

Computational Complexity · Computer Science 2011-01-24 Hector Zenil

We Propose A Novel Automaton Model which uses Arithmetic Operations as the Evolving Rules, each cell has the states of the Natural Numbers k = (N), a radius of r = 1/2 and operates on an arbitrary input size. The Automaton reads an…

Formal Languages and Automata Theory · Computer Science 2017-05-18 Abdulrhman Elnekiti

Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…

Statistical Mechanics · Physics 2019-01-01 Adam Rupe , James P. Crutchfield

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

Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…

Group Theory · Mathematics 2025-02-27 Tawfiq Hamed , Mohammad Saleh

We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…

Discrete Mathematics · Computer Science 2018-07-17 Pablo Arrighi , Clément Chouteau , Stefano Facchini , Simon Martiel

We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…

Dynamical Systems · Mathematics 2017-02-21 Martin Delacourt , Benjamin Hellouin de Menibus

Cellular automata can simulate many complex physical phenomena using the power of simple rules. The presented methodological platform expresses the concept of programmable matter in which Newtons laws of motion are one of examples. Energy…

Cellular Automata and Lattice Gases · Physics 2023-01-10 Krzysztof Pomorski , Dariusz Kotula

We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the…

Neural and Evolutionary Computing · Computer Science 2023-08-02 Stephen Whitelam , Isaac Tamblyn

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) provide a minimal formalism for investigating how simple local interactions generate rich spatiotemporal behavior in domains as diverse as traffic flow, ecology, tissue morphogenesis and crystal growth. However,…

Machine Learning · Computer Science 2025-06-24 Jaime A. Berkovich , Noah S. David , Markus J. Buehler

Cellular automata provide models of parallel computation based on cells, whose connectivity is given by an action of a monoid on the cells. At each step in the computation, every cell is decorated with a state that evolves in discrete steps…

Logic in Computer Science · Computer Science 2025-12-17 Henning Basold , Chase Ford , Lulof Pirée

Cellular automata are discrete and computational models thatcan be shown as general models of complexity. They are used in varied applications to derive the generalized behavior of the presented model. In this paper we have took one such…

Neural and Evolutionary Computing · Computer Science 2020-05-14 Karan Nayak

We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…

Statistical Mechanics · Physics 2023-12-05 Franco Bagnoli , Raul Rechtman

A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…

Cellular Automata and Lattice Gases · Physics 2012-03-20 Vladimir Garcia-Morales

We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in…

adap-org · Physics 2015-06-30 James P. Crutchfield , Melanie Mitchell , Rajarshi Das