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Related papers: Topological Dynamics of 2D Cellular Automata

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We study some dynamical properties of a family of two-dimensional cellular automata: those that arise from an underlying one dimensional sand automaton whose local rule is obtained using a latin square. We identify a simple sand automaton G…

Dynamical Systems · Mathematics 2012-05-18 Nicholas Faulkner , Reem Yassawi

Cellular automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and…

Cellular Automata and Lattice Gases · Physics 2018-10-09 Junfang Tian , Chenqiang Zhu , Rui Jiang

The prediction of the behavior of the disease, the level of affectation in a population and the ways to control it are the most important aspects studied by epidemiology using tools such as historical data and mathematical models. So, our…

Dynamical Systems · Mathematics 2022-04-04 Jorge Andrés Ibáñez Huertas , Carlos Isaac Zainea Maya

We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique. We introduce a general framework for algebraic construction of renormalization groups (RG) on cellular automata and apply…

Statistical Mechanics · Physics 2011-08-22 Erik Edlund , Martin Nilsson Jacobi

Probabilistic cellular automata (CA) provides a classic framework for studying non-equilibrium statistical physics on a lattices. A notable example is the Domany-Kinzel CA, which has been used to investigate the process of directed…

Quantum Physics · Physics 2022-04-26 Ramil Nigmatullin , Elisabeth Wagner , Gavin K. Brennen

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

Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…

Dynamical Systems · Mathematics 2025-09-03 Nassima Ait Sadi , Rezki Chemlal

Elementary Cellular Automata (ECA) are a well-studied computational universe that is, despite its simple configurations, capable of impressive computational variety. Harvesting this computation in a useful way has historically shown itself…

Cellular Automata and Lattice Gases · Physics 2024-07-26 Tom Eivind Glover , Ruben Jahren , Francesco Martinuzzi , Pedro Gonçalves Lind , Stefano Nichele

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

The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…

Cellular Automata and Lattice Gases · Physics 2016-08-22 T. E. Raptis

Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize…

Computational Complexity · Computer Science 2008-08-13 Sudhakar Sahoo , Pabitra Pal Choudhury , Mithun Chakraborty

We introduce the property of pre-expansivity for cellular automata (CA): it is the property of being expansive on asymptotic pairs of configurations (i.e. configurations that differ in only finitely many positions). Pre-expansivity…

Discrete Mathematics · Computer Science 2019-11-07 A. Gajardo , V. Nesme , Guillaume Theyssier

One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…

Cellular Automata and Lattice Gases · Physics 2025-12-10 Martin Schaller , Karl Svozil

We study the synchronization of totalistic one dimensional cellular automata (CA). The CA with a non zero synchronization threshold exhibit complex non periodic space time patterns and conversely. This synchronization transition is related…

Statistical Mechanics · Physics 2007-05-23 Franco Bagnoli , Raul Rechtman

We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state $\sigma_i(t) \in \{0,1\}$ of a cell $i$ does not only depend on the states in its local neighborhood at time $t-1$, but also on the memory of…

Statistical Mechanics · Physics 2007-05-23 Thimo Rohlf , Constantino Tsallis

This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…

Symplectic Geometry · Mathematics 2012-03-22 Stefan Müller , Peter Spaeth

We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations…

Formal Languages and Automata Theory · Computer Science 2015-05-13 Genaro J. Martinez , Andrew Adamatzky , Harold V. McIntosh

We investigate a cellular automaton (CA) model of traffic on a bi-directional two-lane road. Our model is an extension of the one-lane CA model of {Nagel and Schreckenberg 1992}, modified to account for interactions mediated by passing, and…

Statistical Mechanics · Physics 2009-10-31 Patrice Simon , Howard A Gutowitz

In Isliker et al. (2000b), an extended cellular automaton (X-CA) model for solar flares was introduced. In this model, the interpretation of the model's grid-variable is specified, and the magnetic field, the current, and an approximation…

Astrophysics · Physics 2009-11-07 H. Isliker , A. Anastasiadis , L. Vlahos

We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable injectivity, stable reversibility, stable post-surjectivity…

Dynamical Systems · Mathematics 2022-03-03 Xuan Kien Phung