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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

A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…

Cellular Automata and Lattice Gases · Physics 2010-03-26 Xin-She Yang , Young Z. L. Yang

Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is…

Logic in Computer Science · Computer Science 2008-02-28 Birendra Kumar Nayak , Sudhakar Sahoo , Sushant Kumar Rout

A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations).…

Cellular Automata and Lattice Gases · Physics 2016-09-20 Genaro J. Martinez , Andrew Adamatzky , Harold V. McIntosh

Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…

Cellular Automata and Lattice Gases · Physics 2020-01-20 William Gilpin

Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by…

Combinatorics · Mathematics 2025-03-14 Luca Manzoni , Luca Mariot , Giuliamaria Menara

This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all…

Cellular Automata and Lattice Gases · Physics 2019-07-16 Markus Redeker

A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing…

Formal Languages and Automata Theory · Computer Science 2011-02-15 Julien Cervelle , Enrico Formenti , Pierre Guillon

A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…

Cellular Automata and Lattice Gases · Physics 2007-05-23 J. R. Sanchez , R. Lopez-Ruiz

An "odd-rule" cellular automaton (CA) is defined by specifying a neighborhood for each cell, with the rule that a cell turns ON if it is in the neighborhood of an odd number of ON cells at the previous generation, and otherwise turns OFF.…

Combinatorics · Mathematics 2015-03-24 Shalosh B. Ekhad , N. J. A. Sloane , Doron Zeilberger

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

The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…

Cellular Automata and Lattice Gases · Physics 2007-05-23 J. R. Sanchez , R. Lopez-Ruiz

Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…

Formal Languages and Automata Theory · Computer Science 2009-07-30 Martin Kutrib , Andreas Malcher

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

A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority…

Pattern Formation and Solitons · Physics 2016-05-25 Vladimir García-Morales

We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…

Computational Physics · Physics 2025-02-05 Lander Besabe , Editha Jose , Alvin Karlo Tapia

Rule 22 elementary cellular automaton (ECA) has a 3--cell neighborhood, binary cell states, where a cell takes state `1' if there is exactly one neighbor, including the cell itself, in state `1'. In Boolean terms the cell-state transition…

Cellular Automata and Lattice Gases · Physics 2020-05-05 Genaro J. Martinez , Andrew Adamatzky , Rolf Hoffmann , Dominique Deserable , Ivan Zelinka

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

The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…

In this paper, we analyze the algebraic structure of some null boundary as well as some periodic boundary 2-D Cellular Automata (CA) rules by introducing a new matrix multiplication operation using only AND, OR instead of most commonly used…

Discrete Mathematics · Computer Science 2008-08-12 Sudhakar Sahoo , Sanjaya Sahoo , Birendra Kumar Nayak , Pabitra Pal Choudhury