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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…

Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…

Statistical Mechanics · Physics 2026-03-31 Mihir Metkar , Neha Sah , Yichen Zhou

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

We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…

Cellular Automata and Lattice Gases · Physics 2009-11-13 Nino Boccara

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

This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…

Computational Complexity · Computer Science 2015-12-22 Yoshihiko Kayama

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

In this paper, we mainly study linear one-dimensional and two-dimensional elementary cellular automata that generate symmetrical spatio-temporal patterns. For spatio-temporal patterns of cellular automata from the single site seed, we…

Cellular Automata and Lattice Gases · Physics 2022-07-20 Akane Kawaharada

Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…

Cellular Automata and Lattice Gases · Physics 2023-10-03 Lei Kou , Fangfang Zhang , Luobing Chen , Wende Ke , Quande Yuan , Junhe Wan , Zhen Wang

We show that there exists a one-to-one correspondence between the set of number-conserving cellular automata (CA) with $q$ inputs and the set of balanced sequences with $q$ terms. This allows to enumerate number-conserving CA. We also show…

Cellular Automata and Lattice Gases · Physics 2007-11-09 Henryk Fuks , Kate Sullivan

In this paper, we develop a new cellular automata-based linear model for several nonlinear pseudorandom number generators with practical applications in symmetric cryptography. Such a model generates all the solutions of linear binary…

Cryptography and Security · Computer Science 2010-05-04 Pino Caballero-Gil , Amparo Fúster-Sabater , Oscar Delgado-Mohatar

This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…

Discrete Mathematics · Computer Science 2008-04-16 Pabitra Pal Choudhury , Birendra Kumar Nayak , Sudhakar Sahoo , Sunil Pankaj Rath

This paper studies the number conservation property of 1-dimensional non-uniform cellular automata (CAs). In a non-uniform cellular automaton (CA), different cells may follow different rules. The present work considers that the cells follow…

Formal Languages and Automata Theory · Computer Science 2016-04-25 Raju Hazari , Sukanta Das

Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…

Cellular Automata and Lattice Gases · Physics 2023-08-15 Abhishek Dalai

This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are pseudo-random noise sequences with application in…

Cryptography and Security · Computer Science 2015-03-17 A. Fúster-Sabater , P. Caballero-Gil

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…

Machine Learning · Computer Science 2021-10-28 Daniele Grattarola , Lorenzo Livi , Cesare Alippi

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

Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…

Discrete Mathematics · Computer Science 2008-09-11 Donny Cheung , Carlos A. Perez-Delgado

Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…

Cellular Automata and Lattice Gases · Physics 2025-06-02 Markus Redeker

While one-dimensional cellular automata have been well studied, there are relatively few results about multidimensional cellular automata; the investigation of cellular automata defined on Cayley trees constitutes an intermediate class.…

Dynamical Systems · Mathematics 2017-01-11 Chih-Hung Chang , Jing-Yi Su
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