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Related papers: 2D Hexagonal Cellular Automata: The Complexity of …

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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 concerns $d$-dimensional cellular automata with the von Neumann neighborhood that conserve the sum of the states of all their cells. These automata, called number-conserving or density-conserving cellular automata, are of…

Mathematical Physics · Physics 2020-08-26 Barbara Wolnik , Anna Nenca , Jan M. Baetens , Bernard De Baets

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 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

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

The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D square lattice much like Conway's Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution…

Cellular Automata and Lattice Gases · Physics 2012-03-09 Nathaniel Johnston

Hierarchical structure is an essential part of complexity, important notion relevant for a wide range of applications ranging from biological population dynamics through robotics to social sciences. In this paper we propose a simple…

Populations and Evolution · Quantitative Biology 2015-06-26 Ivan Gotz , Isaak Rubinstein , Eugene Tsvetkov , Boris Zaltzman

This paper describes a new concept of cellular automaton (CA). XCA consists of a set of arcs (edges) that correspond to cells in CA. At a particular time, the arcs are connected to a directed graph. With each time step, the arcs exchange…

Cellular Automata and Lattice Gases · Physics 2016-07-19 Walter Eckel

Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…

Neural and Evolutionary Computing · Computer Science 2023-01-04 Marlene Grieskamp , Chaytan Inman , Shaun Lee

Motivated by questions in biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. We investigate what sort of self-stabilising…

Formal Languages and Automata Theory · Computer Science 2009-11-14 Alan Gibbons , Martyn Amos

In order to develop systems capable of modeling artificial life, we need to identify, which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time…

Cellular Automata and Lattice Gases · Physics 2020-09-01 Barbora Hudcova , Tomas Mikolov

We present a new Life-like cellular automaton (CA) capable of logic universality -- the X-rule. The CA is 2D, binary, with a Moore neighborhood and $\lambda$ parameter similar to the game-of-Life, but is not based on birth/survival and is…

Cellular Automata and Lattice Gases · Physics 2017-09-11 José Manuel Gómez Soto , Andrew Wuensche

Cellular automata are computers, similar to Turing machines. The main difference is that Turing machines use a one-dimensional tape, whereas cellular automata use a two-dimensional grid. The best-known cellular automaton is the Game of…

Cellular Automata and Lattice Gases · Physics 2025-01-10 Peter Turney

We present herein an introduction to implementing 2-color cellular automata on quantum annealing systems, such as the D-Wave quantum computer. We show that implementing nearest-neighbor cellular automata is possible. We present an…

Quantum Physics · Physics 2021-01-08 Robert A. Dunn

The local rules of Wolfram cellular automata with one-dimensional three-cell neighborhoods are represented by eight-bit binary that encode deterministic update rules. These automata are widely utilized to investigate self-organization…

Computational Physics · Physics 2025-09-15 Kui Tuo , Shengfeng Deng , Yuxiang Yang , Yanyang Wang , Qiuping A. Wang , Wei Li , Wenjun Zhang

Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…

Quantum Physics · Physics 2008-11-04 Ioannis G. Karafyllidis

In previous works, hexagonal cellular automata (CA) have been studied as a variation of the famous Game of Life CA, mainly for spiral phenomena simulations; where the most interesting constructions are related to the Belousov-Zhabotinsky…

Cellular Automata and Lattice Gases · Physics 2014-11-05 Rogelio Basurto , Paulina A. León , Genaro J. Martínez , Juan C. Seck-Tuoh-Mora

Neural Cellular Automata (NCAs) have been proven effective in simulating morphogenetic processes, the continuous construction of complex structures from very few starting cells. Recent developments in NCAs lie in the 2D domain, namely…

Machine Learning · Computer Science 2021-06-07 Shyam Sudhakaran , Djordje Grbic , Siyan Li , Adam Katona , Elias Najarro , Claire Glanois , Sebastian Risi

The emergence of complex structures in the systems governed by a simple set of rules is among the most fascinating aspects of Nature. The particularly powerful and versatile model suitable for investigating this phenomenon is provided by…

Adaptation and Self-Organizing Systems · Physics 2023-10-11 Jarosław Adam Miszczak

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in…

Artificial Intelligence · Computer Science 2010-11-23 Andrew Adamatzky , Larry Bull , Pierre Collet , Emmanuel Sapin