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Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are…

Neural and Evolutionary Computing · Computer Science 2021-07-13 Alexandre Variengien , Stefano Nichele , Tom Glover , Sidney Pontes-Filho

Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…

Symbolic Computation · Computer Science 2015-03-24 Matthew England , David Wilson

We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The…

Quantum Physics · Physics 2015-08-03 Hans-Thomas Elze

Cellular automata (CAs) and convolutional neural networks (CNNs) are closely related due to the local nature of information processing. The connection between these topics is beneficial to both related fields, for conceptual as well as…

Cellular Automata and Lattice Gases · Physics 2024-09-05 Michiel Rollier , Aisling J. Daly , Odemir M. Bruno , Jan M. Baetens

Over an arbitrary commutative ring $R$, we develop a theory of quantum cellular automata. We then use algebraic K-theory to construct a space $\mathbf{Q}(X)$ of quantum cellular automata (QCA) on a given metric space $X$. In most cases of…

Algebraic Topology · Mathematics 2026-03-04 Mattie Ji , Bowen Yang

In this work we provide analytic results of infinite one-dimensional cellular automaton(CA). By realizing symbolic products, we investigate a subclass of infinite CA and prove analytically that within this subclass the only allowed…

Cellular Automata and Lattice Gases · Physics 2009-11-07 Ru-Fen Liu , Chia-Chu Chen

One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…

Quantum Physics · Physics 2008-04-15 Pablo Arrighi , Vincent Nesme , Reinhard Werner

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of…

Quantum Physics · Physics 2010-10-13 Pablo Arrighi , Jonathan Grattage

We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial…

Quantum Physics · Physics 2008-12-10 Pablo Arrighi , Renan Fargetton , Zizhu Wang

The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem. In this paper we present a new two-dimensional CA model for solid dynamics. In this model the solid body is represented by a set of…

Cellular Automata and Lattice Gases · Physics 2015-06-12 Yinfeng Dong , Guangcai Zhang , Aiguo Xu , Yanbiao Gan

The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between…

Computational Complexity · Computer Science 2021-02-05 Augusto Modanese

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

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

Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…

A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…

Cryptography and Security · Computer Science 2010-06-15 Debasis Das , Abhishek Ray

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

We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in…

adap-org · Physics 2015-06-30 James P. Crutchfield , Melanie Mitchell , Rajarshi Das

Cellular automata have long been celebrated for their ability to generate complex behaviors from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements…

Machine Learning · Computer Science 2025-05-22 Gabriel Béna , Maxence Faldor , Dan F. M. Goodman , Antoine Cully

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

Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…

Discrete Mathematics · Computer Science 2014-05-22 Pablo Arrighi , Simon Martiel , Vincent Nesme