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Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems. The most widely known form of CA, the elementary cellular automaton (ECA), has been…

Cellular Automata and Lattice Gases · Physics 2013-10-15 Lucas Kang

This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the…

adap-org · Physics 2009-10-30 Nino Boccara , Henryk Fuks

Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…

Statistical Mechanics · Physics 2025-09-30 Annie Ray , Raymond Laflamme , Aleksander Kubica

We study one dimensional binary Probabilistic Cellular Automaton (PCA) that interpolate between Wolfram's classical rules 23, 77, 178 and 232. These rules are the only ones that satisfy two criteria: (i) in the case of a majority in the…

Cellular Automata and Lattice Gases · Physics 2026-05-19 Francisco J. Muñoz , Juan Carlos Nuño

Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…

Systems and Control · Electrical Eng. & Systems 2025-07-01 Faizal Hafiz , Amelia Kunze , Enrico Formenti , Davide La Torre

In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…

Condensed Matter · Physics 2007-05-23 Kristian Lindgren , Cristopher Moore , Mats G. Nordahl

We show how to construct a deterministic nearest-neighbour cellular automaton (CA) with four states which emulates diffusion on a one-dimensional lattice. The pseudo-random numbers needed for directing random walkers in the diffusion…

Cellular Automata and Lattice Gases · Physics 2023-12-19 Henryk Fukś

We study a family of deterministic models for highway traffic flow which generalize cellular automaton rule 184. This family is parametrized by the speed limit $m$ and another parameter $k$ that represents a ``degree of aggressiveness'' in…

adap-org · Physics 2009-10-30 Henryk Fuks , Nino Boccara

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…

The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a…

Statistical Mechanics · Physics 2009-11-07 Boris S. Kerner , Sergey L. Klenov , Dietrich E. Wolf

It is shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a non-decreasing function of time. This result is…

Disordered Systems and Neural Networks · Physics 2016-12-21 Nino Boccara

Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under…

Discrete Mathematics · Computer Science 2007-06-19 Damien Regnault , Nicolas Schabanel , Éric Thierry

Agent-based (AB) or Cellular Automata (CA) models are rule based and are a relatively simple discrete method that can be used to simulate complex interactions of many agents or cells. The relative ease of implementing the computational…

Dynamical Systems · Mathematics 2019-09-11 Michael A. Yereniuk , Sarah D. Olson

A system of agents moving along a road in both directions is studied numerically within a cellular-automata formulation. An agent steps to the right with probability $q$ or to the left with $1-q$ when encountering other agents. Our model is…

Physics and Society · Physics 2009-07-17 Seung Ki Baek , Petter Minnhagen , Sebastian Bernhardsson , Kweon Choi , Beom Jun Kim

We present a sequential cellular automaton of radius 2 1 as a solution to the density classification task that makes use of an intermediate alphabet, and converges to a clean fixed point with no remaining auxiliary or intermediate…

Discrete Mathematics · Computer Science 2024-09-11 Pacôme Perrotin , Pedro Paulo Balbi , Eurico Ruivo

Traffic models based on cellular automata have high computational efficiency because of their simplicity in describing unrealistic vehicular behavior and the versatility of cellular automata to be implemented on parallel processing. On the…

Multiagent Systems · Computer Science 2013-02-05 Emanuele Rodaro , Öznur Yeldan

A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the…

comp-gas · Physics 2009-10-31 A. Awazu

A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…

Cellular Automata and Lattice Gases · Physics 2025-05-30 Rolf Hoffmann , Mariusz Białecki

A family of multi-value cellular automaton (CA) associated with traffic flow is presented in this paper. The family is obtained by extending the rule-184 CA, which is an ultradiscrete analogue to the Burgers equation. CA models in the…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Katsuhiro Nishinari , Daisuke Takahashi

We investigate one-dimensional Probabilistic Cellular Automata, called Diploid Elementary Cellular Automata (DECA), obtained as random mixture of two different Elementary Cellular Automata rules. All the cells are updated synchronously and…

Statistical Mechanics · Physics 2021-04-28 Emilio N. M. Cirillo , Francesca R. Nardi , Cristian Spitoni