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We show how the trajectories of $d$-dimensional cellular automata (CA) can be used to determine the ground states of $(d+1)$-dimensional classical spin models, and we characterise their quantum phase transition, when in the presence of a…

Statistical Mechanics · Physics 2025-07-31 Konstantinos Sfairopoulos , Luke Causer , Jamie F. Mair , Juan P. Garrahan

This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…

Dynamical Systems · Mathematics 2025-12-10 B. Wolnik , D. M. Falkiewicz , W. Bołt , A. Rutkowski , B. De Baets

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

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

A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…

Cellular Automata and Lattice Gases · Physics 2016-06-09 Vladimir García-Morales

Individual cellular automata rules are attractive models for a range of biological and physical self-assembling systems. While coexpression and coevolution are common in such systems, ensembles of cellular automata rules remain poorly…

Cellular Automata and Lattice Gases · Physics 2007-07-26 Alexander D. Wissner-Gross

Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize…

Computational Complexity · Computer Science 2008-08-13 Sudhakar Sahoo , Pabitra Pal Choudhury , Mithun Chakraborty

We present time-constrained automata (TCA), a model for hard real-time computation in which agents behaviors are modeled by automata and constrained by time intervals. TCA actions can have multiple start time and deadlines, can be…

Logic in Computer Science · Computer Science 2010-10-28 Matthieu Lemerre , Vincent David , Christophe Aussaguès , Guy Vidal-Naquet

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

A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…

Cryptography and Security · Computer Science 2010-06-15 Debasis Das , Abhishek Ray

Cellular automata (CA) have been found as an attractive modeling tool for various applications, such as, pattern recognition, image processing, data compression, encryption, and specially for VLSI design & test. For such applications,…

Formal Languages and Automata Theory · Computer Science 2013-11-28 Sukanta Das , Biplab K Sikdar

A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…

Quantum Physics · Physics 2021-08-03 Pedro C. S. Costa

A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…

Quantum Physics · Physics 2017-06-06 Hans-Thomas Elze

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

Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of…

Artificial Intelligence · Computer Science 2025-06-26 Salvatore Milite , Giulio Caravagna , Andrea Sottoriva

We study networks representing the dynamics of elementary 1-d cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node…

Statistical Mechanics · Physics 2009-11-11 Amer Shreim , Peter Grassberger , Walter Nadler , Björn Samuelsson , Joshua E. S. Socolar , Maya Paczuski

This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…

We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions…

Probability · Mathematics 2012-09-27 Cory Hauck , Yi Sun , Ilya Timofeyev

Previous study of cellular automata and random Boolean networks has shown emergent behavior occurring at the edge of chaos where the randomness (disorder) of internal connections is set to an intermediate critical value. The value at which…

Cellular Automata and Lattice Gases · Physics 2023-04-17 Ron Fulbright

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