Nonvanishing optimal noise in cellular automaton model of self-propelled particles

Du, Guangle; Ye, Fang-Fu

doi:10.1088/1674-1056/ac67c4

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…Several papers have used the mean-field approximation to characterize CAs with gliders, but only for specific cases [23][24][25][26], in conjunction with other analysis tools [11] or limited to ECAs [27,28]. This paper aims to enrich the mean-field approach by identifying CAs with gliders in ECAs and automata with a larger number of states, making it a first attempt of its kind.…”

Section: Introductionmentioning

confidence: 99%

Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata

Seck-Tuoh-Mora,

Medina-Marin,

Hernández-Romero

et al. 2023

Mathematics

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Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system. This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata.

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Section: Introductionmentioning

confidence: 99%

Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata

Seck-Tuoh-Mora,

Medina-Marin,

Hernández-Romero

et al. 2023

Mathematics

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Noise-induced phase transition in the Vicsek model through eigen microstate methodology

Jia 贾,

Han 韩,

Li 李

2024

Chinese Phys. B

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This paper presents a comprehensive framework for analyzing phase transitions in collective models like the Vicsek model under various noise types. The Vicsek model, focuses on understanding the collective behaviors of social animals, is known for its discontinuous phase transitions under vector noise. However, its behavior under scalar noise remains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and non-equilibrium state, the eigen microstate method is employed here for a quantitative examination of the phase transitions in the Vicsek model under both vector and scalar noise. The study finds that the Vicsek model exhibits discontinuous phase transitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for these phase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions with the escalation of population density.

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Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata

Seck-Tuoh-Mora,

Medina-Marin,

Hernández-Romero

et al. 2023

Preprint

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Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system.This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata.

show abstract

Nonvanishing optimal noise in cellular automaton model of self-propelled particles

Cited by 3 publications

References 27 publications

Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata

Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata

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