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Related papers: Cellular Automata and Discrete Geometry

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We examine a simple two lane cellular automaton based upon the single lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of…

Condensed Matter · Physics 2015-06-25 Marcus Rickert , Kai Nagel , Michael Schreckenberg , Andreas Latour

In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich…

Cellular Automata and Lattice Gases · Physics 2010-07-27 Zan Pan

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

This paper explores the use of 2D cellular automata (CA) to generate 3D terrains through a simple additive approach. Experimenting with multiple CA transition rules produced aesthetically interesting, navigable landscapes, suggesting…

Cellular Automata and Lattice Gases · Physics 2025-08-22 Nuno Fachada , António R. Rodrigues , Diogo de Andrade , Phil Lopes

Nielsen, et al. [1, 2] proposed a view of quantum computation where determining optimal algorithms is equivalent to extremizing a geodesic length or cost functional. This view of optimization is highly suggestive of an action principle of…

Quantum Physics · Physics 2012-08-17 Jonathan R. McDonald , Paul M. Alsing , Howard A. Blair

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

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

We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically…

Cellular Automata and Lattice Gases · Physics 2009-11-13 Carsten Marr , Marc-Thorsten Huett

A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…

Cellular Automata and Lattice Gases · Physics 2015-08-03 Vladimir Garcia-Morales

Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems…

Statistical Mechanics · Physics 2009-10-30 Kai Nagel , Dietrich E Wolf , Peter Wagner , Patrice Simon

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

This paper presents an application of the Infinite Unit Axiom, introduced by Yaroslav Sergeyev, (see [11] - [14]) to the development of one-dimensional cellular automata. This application allows the establishment of a new and more precise…

Discrete Mathematics · Computer Science 2011-10-28 Louis D'Alotto

The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and…

Cellular Automata and Lattice Gases · Physics 2024-05-10 Alexander Yu. Vlasov

Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…

Cellular Automata and Lattice Gases · Physics 2025-01-14 Alexey Kazarnikov , Nadja Ray , Heikki Haario , Joona Lappalainen , Andreas Rupp

Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…

Group Theory · Mathematics 2025-02-27 Tawfiq Hamed , Mohammad Saleh

A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…

Cellular Automata and Lattice Gases · Physics 2015-06-17 Vladimir Garcia-Morales

The goal of this paper is to present a solution of the cellular automaton associated with the discrete KdV equation using algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve.

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Mariusz Bialecki

A realization of discrete conjugate net is presented by using correlation functions of strings in a gauge covariant form.

solv-int · Physics 2007-05-23 Satoru Saito

We study the problem of sequentializing a cellular automaton without introducing any intermediate states, and only performing reversible permutations on the tape. We give a decidable characterization of cellular automata which can be…

Dynamical Systems · Mathematics 2018-04-09 Jarkko Kari , Ville Salo , Thomas Worsch

In this exploratory paper we introduce the problem of cognitive agents that learn how to modify their environment according to local sensing to reach a global goal. We concentrate on discrete dynamics (cellular automata) on a…

Cellular Automata and Lattice Gases · Physics 2026-04-14 Franco Bagnoli , Bassem Sellami , Amira Mouakher , Samira El Yacoubi