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This paper presents solutions to Density Classification Task (DCT) using a variant of Cellular Automata (CA) called Programmable Cellular Automata (PCA). The translation property as well as the density preserving property of fundamental CA…

Cellular Automata and Lattice Gases · Physics 2009-02-17 Sudhakar Sahoo , Pabitra Pal Choudhury , Amita Pal , Birendra Kumar Nayak

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

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular…

Probability · Mathematics 2011-11-22 Ana Busic , Nazim Fates , Jean Mairesse , Irene Marcovici

We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton's transition function. These behavioral metrics are formulated to satisfy…

Formal Languages and Automata Theory · Computer Science 2015-01-19 Juan C. López-González , Antonio Rueda-Toicen

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 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

The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules…

Mathematical Physics · Physics 2007-05-23 Vladimir V. Kornyak

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…

Formal Languages and Automata Theory · Computer Science 2015-08-20 Witold Bołt , Jan M. Baetens , Bernard DeBaets

We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…

Probability · Mathematics 2015-09-30 Janko Gravner , Alexander E. Holroyd

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

We study the dynamics of (synchronous) one-dimensional cellular automata with cyclical boundary conditions that evolve according to the majority rule with radius $ r $. We introduce a notion that we term cell stability with which we express…

Discrete Mathematics · Computer Science 2022-06-06 Yonatan Nakar , Dana Ron

We study one-dimensional cellular automata whose rules are chosen at random from among $r$-neighbor rules with a large number $n$ of states. Our main focus is the asymptotic behavior, as $n \to \infty$, of the longest temporal period…

Probability · Mathematics 2019-09-17 Janko Gravner , Xiaochen Liu

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…

Cellular Automata and Lattice Gases · Physics 2023-12-18 Henryk Fukś , Andrew Skelton

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

We study cellular automata with randomly selected rules. Our setting are two-neighbor rules with a large number $n$ of states. The main quantity we analyze is the asymptotic probability, as $n \to \infty$, that the random rule has a…

Probability · Mathematics 2019-09-17 Janko Gravner , Xiaochen Liu

We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration…

Cellular Automata and Lattice Gases · Physics 2015-05-18 Masahiro Kanai

This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…

Computational Complexity · Computer Science 2007-05-23 Maxim Makatchev

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…

Cellular Automata and Lattice Gases · Physics 2023-12-18 Henryk Fukś

In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…

Cellular Automata and Lattice Gases · Physics 2007-07-06 Xu Xu , Yi Song , Stephen P. Banks

It has been shown that uniform as well as non-uniform cellular automata (CA) can be evolved to perform certain computational tasks. Random Boolean networks are a generalization of two-state cellular automata, where the interconnection…

Disordered Systems and Neural Networks · Physics 2007-05-23 Bertrand Mesot , Christof Teuscher