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Related papers: Number-conserving cellular automaton rules

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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

The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approximation works surprisingly well for some cellular automata,…

Cellular Automata and Lattice Gases · Physics 2026-01-05 Henryk Fukś , Yucen Jin

We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…

Adaptation and Self-Organizing Systems · Physics 2017-06-29 Amitava Banerjee , Muktish Acharyya

Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears…

Cellular Automata and Lattice Gases · Physics 2015-06-26 Nino Boccara , Henryk Fuks

We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…

Cellular Automata and Lattice Gases · Physics 2009-11-10 Henryk Fukś

A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…

Cellular Automata and Lattice Gases · Physics 2015-06-12 Malgorzata J. Krawczyk , Krzysztof Kulakowski

In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…

Cellular Automata and Lattice Gases · Physics 2017-04-04 Henryk Fukś , Joel Midgley-Volpato

A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.

Cellular Automata and Lattice Gases · Physics 2012-06-12 Daniel B. Miller , Edward Fredkin

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5…

Formal Languages and Automata Theory · Computer Science 2016-10-04 Katsunobu Imai , Hisamichi Ishizaka , Victor Poupet

Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…

Quantum Physics · Physics 2016-04-25 Hans-Thomas Elze

We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one…

Probability · Mathematics 2011-01-07 F. M. Dekking , L. van Driel , A. Fey

We propose a characteristic representation ofone-dimensional and 2-state, 3-neighbor cellular automaton rules, which describes an effective form of each rule after many time steps. Simulated results of the representation show that complex…

chao-dyn · Physics 2008-02-03 Y. Kayama , H. Anada , Y. Imamura , 9 pages

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

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…

Probability · Mathematics 2024-01-26 Peter Gacs

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 a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…

Cellular Automata and Lattice Gases · Physics 2023-05-12 Luca Bertolani , Andrea Idini

A one-dimensional two-state number-conserving cellular automaton (NCCA) is a cellular automaton whose states are 0 or 1 and where cells take states 0 and 1 and updated their states by the rule which keeps overall sum of states constant. It…

Cellular Automata and Lattice Gases · Physics 2019-10-21 Gil-Tak Kong , Katsunobu Imai , Toru Nakanashi

We examine various realistic generalizations of the basic cellular automaton model describing traffic flow along a highway. In particular, we introduce a {\em slow-to-start} rule which simulates a possible delay before a car pulls away from…

Condensed Matter · Physics 2009-10-28 Simon C. Benjamin , Neil F. Johnson , P. M. Hui

A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…

Cellular Automata and Lattice Gases · Physics 2017-08-14 Marek Pietrow

In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…

Soft Condensed Matter · Physics 2007-05-23 M. E. Larraga , J. A. del Rio