Volume 33, Number 3 (2024)

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Triangular Automata: The 256 Elementary Cellular Automata of the Two-Dimensional Plane
Paul Cousin

Cellular automata (CAs) in the triangular grid are here called triangular automata (TAs). This paper focuses on the simplest type of TAs, called elementary TAs (ETAs). They are argued to be the two-dimensional counterpart of Wolfram’s elementary CAs. Conceptual and computational tools for their study are presented, along with an initial analysis. This paper is accompanied by the author’s website [1], where the results can be explored interactively. The source code is available in the form of a Wolfram Language package at [2].

Keywords: cellular automata; triangular grid; dynamical systems; complexity

Cite this publication as:
P. Cousin, “Triangular Automata: The 256 Elementary Cellular Automata of the Two-Dimensional Plane,” Complex Systems, 33(3), 2024 pp. 253–276.
https://doi.org/10.25088/ComplexSystems.33.3.253

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Exploration of Genotype-Phenotype Relationships in Nontotalistic Cellular Automata Using HexCode, a Novel Rule Encoding System
Hans H. Zingg

The spacetime evolution of a cellular automaton (CA) is determined by its rule table. Whereas a rule table is analogous to the DNA of the CA, that is, its genotype, the resulting spacetime evolution is equivalent to its phenotype. Conventional rule codes carry no easily recognizable features that would allow establishing a relationship between the rule genotype and the rule phenotype. This is particularly relevant for totalistic cellular automata (CAs) with radii and dimensions greater than one where the rule space is rapidly expanding. Here, a universal rule code, called HexCode, has been created that enables a hitherto unachievable systematic and exhaustive exploration of geometric features of CA phenotypes based on their genotypes in the large rule spaces of totalistic CAs with radii and dimensions greater than one.

Keywords: cellular automata; genotype/phenotype relationships; rule encoding  

Cite this publication as:
H. H. Zingg, “Exploration of Genotype-Phenotype Relationships in Nontotalistic Cellular Automata Using HexCode, a Novel Rule Encoding System,” Complex Systems, 33(3), 2024 pp. 277–318.
https://doi.org/10.25088/ComplexSystems.33.3.277

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Forgiveness Is an Adaptation in the Iterated Prisoner's Dilemma with Memory
Meliksah Turker and Haluk O. Bingol

The prisoner’s dilemma (PD) is used to represent many real-life phenomena, whether from the civilized world of humans or from the wild world of other living things. Researchers working on the iterated prisoner’s dilemma (IPD) with limited memory inspected the outcome of different forgetting strategies in a homogeneous environment, within which all agents adopt the same forgetting strategy at the same time. In this paper, with the intention to represent real life more realistically, we improve existing forgetting strategies, offer new ones, conduct experiments in a heterogeneous environment that contains mixed agents and compare the results with previous research, as well as conduct experiments in a homogeneous environment via agent-based stochastic simulations. Our findings show that the outcome depends on the type of environment and is just the opposite for homogeneous and heterogeneous ones, opposing the existing literature on the IPD. Consequently, forgetting and forgiving defectors is the supreme memory management strategy in a competitive, heterogeneous environment. Therefore, forgiveness is an adaptation.

Keywords: IPD; iterated prisoner’s dilemma; agent-based simulation; PD; prisoner’s dilemma; limited memory; memory management strategy; forgetting strategy  

Cite this publication as:
M. Turker and H. O. Bingol, “Forgiveness Is an Adaptation in the Iterated Prisoner’s Dilemma with Memory,” Complex Systems, 33(3), 2024 pp. 319–332.
https://doi.org/10.25088/ComplexSystems.33.3.319

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Understanding the Role of Daily Activities in the Transmission of COVID-19 in Urban Settings Using an Agent-Based Model
L. L. Lima, E. F. Wanner and A. P. F. Atman

The COVID-19 pandemic has caused widespread disruption and prompted the implementation of nonpharmaceutical measures in several countries to contain the spread of the disease until a vaccine became available. Urban mobility reduction has historically been employed to limit the transmission of epidemics. However, only some studies have quantified the effectiveness of such restrictions across different sectors of society. To address this gap, we have adapted an agent-based model that utilizes data from the Google Community Mobility Report to simulate the dynamics of COVID-19 across 14 Brazilian capitals. Each agent in the model has a network of contacts established from mobility data across various categories. We simulated six scenarios for each capital, each with different probabilities of contagion in each category. Our findings show that different scenarios are more effective in describing the curve of infected people and deaths in each city. In particular, our results indicate that the same scenario was optimal for describing the number of cases and deaths in Belo Horizonte. However, the first peak in the number of deaths could not be reproduced in the model, possibly due to issues with the data recording. Our proposed model can be further developed to incorporate additional elements related to the dynamics of an epidemic and can serve as an additional tool in understanding and planning actions to contain the spread of COVID-19 beyond mobility, particularly in urban centers.

Keywords: SARS-CoV-2; human mobility; agent-based model

Cite this publication as:
L. L. Lima, E. F. Wanner and A. P. F. Atman, “Understanding the Role of Daily Activities in the Transmission of COVID-19 in Urban Settings Using an Agent-Based Model,” Complex Systems, 33(3), 2024 pp. 333–352.
https://doi.org/10.25088/ComplexSystems.33.3.333

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Cellular Automaton-Based Sentiment Analysis Using Deep Learning Methods
Elizabeth M. J. and Raju Hazari

The swift expansion of internet-centric applications, including social media platforms, online marketplaces and blogs, has given rise to comments, experiences, sentiments, evaluations and reviews including daily life events. Sentiment analysis involves the collection of thoughts, opinions, experiences and impressions on diverse areas, including product reviews on e-market sites, movie reviews and experiences on various e-services. The existing solutions encounter various challenges in effectively managing such diverse and nuanced data. So we present a new approach for classifying such sentiments using the cellular automata–based word vectorization method with deep learning techniques such as long short-term memory (LSTM), convolutional neural network (CNN) and CNN-LSTM models. The designed model makes use of pertinent properties of the signals obtained from the cellular automaton to classify sentiments as positive or negative. We consider a grid of cells governed by a synchronous update based on Wolfram’s rules. The cellular automaton evolution process slowly learns the context of the text and reaches a stable state by generating cycle length (CL) signals, after achieving convergence. These signals are used for creating a CL weight matrix. The CL weight matrix is then back-propagated to classify sentiments using standard deep learning methods. The proposed system is a new automated method for assessing semantic linkages and the meaning of the text for natural language applications. LSTM performs well with CL signal weights and produces an accuracy level of 99.18% and an F1_score of 98.68% when trained with sentiment tweets. The experimental results illustrate that the suggested approach has the potential to accurately classify social media comments into different classes and consistently outperforms other baseline models, achieving overall good results.

Keywords: cellular automata; sentiment analysis; machine learning; text vectorization; deep learning

Cite this publication as:
Elizabeth M. J. and R. Hazari, “Cellular Automaton-Based Sentiment Analysis Using Deep Learning Methods,” Complex Systems, 33(3), 2024 pp. 353–385.
https://doi.org/10.25088/ComplexSystems.33.3.353