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In this paper, we prove that there is a strongly universal cellular automaton on the heptagrid with five states under the relaxation of the assumption of rotation invariance for the rules. The result is different from that of a previous paper of the author with six states but with rotationally invariant rules. Here, the structures is more constrained than in the quoted paper with six states and rotation invariance of the rules. [ABSTRACT FROM AUTHOR]

In this paper, we construct a weakly universal cellular automaton in the heptagrid, the tessellation $ \{7,3\} $ { 7 , 3 } which takes place in the hyperbolic plane. The cellular automation is not rotation invariant but which is truly planar. This result, under these conditions, cannot be improved for the tessellations $ \{p,3\} $ { p , 3 } of the hyperbolic plane. [ABSTRACT FROM AUTHOR]

The exploration of the relationship between process parameters and grain evolution during the thermal deformation of rare-earth magnesium alloys using simulation software has significant implications for enhancing research and development efficiency and advancing the large-scale engineering application of high-performance rare-earth magnesium alloys. Through single-pass hot compression experiments, this study obtained high-temperature flow stress curves for rare-earth magnesium alloys, analyzing the variation patterns of these curves and the softening mechanism of the materials. Drawing on physical metallurgical theories, such as the evolution of dislocation density during dynamic recrystallization, recrystallization nucleation, and grain growth, the authors of this paper establish a cellular automaton model to simulate the dynamic recrystallization process by tracking the sole internal variable—the evolution of dislocation density within cells. This model was developed through the secondary development of the DEFORM-3D finite element software. The results indicate that the model established in this study accurately simulates the evolution process of grain growth during heat treatment and the dynamic recrystallization microstructure during the thermal deformation of rare-earth magnesium alloys. The simulated results align well with relevant theories and metallographic experimental results, enabling the simulation of the dynamic recrystallization microstructure and grain size prediction during the deformation process of rare-earth magnesium alloys. [ABSTRACT FROM AUTHOR]

Mean dimension may decrease after taking the natural extension. In this paper we show that mean dimension is preserved by natural extension for an endomorphism on a compact metrizable abelian group. As an application, we obtain that the mean dimension of an algebraic cellular automaton coincides with the mean dimension of its natural extension, which strengthens a result of Burguet and Shi [Israel J. Math. (to appear).] with a different proof. [ABSTRACT FROM AUTHOR]

This paper presents discontinuous Riemann integrable functions on the unit interval $ [0, 1] $ derived from the dynamics of two-dimensional elementary cellular automata. Based on the self-similarities of their orbits, we write down the numbers of nonzero states in the spatial and spatio-temporal patterns and obtain discontinuous Riemann integrable functions by normalizing the values. We calculate the integrals of the two obtained functions over $ [0, 1] $ and demonstrate the relationship between them. [ABSTRACT FROM AUTHOR]

• A modified cellular automaton (CA) model considering the effects of deformation conditions on material parameters was developed using artificial neural network (ANN). • Microstructure evolution of Mg alloy cylindrical part with longitudinal inner ribs (CPLIRs) during hot flow forming was well described by coupling ANN-modified CA and finite element. • Microstructure inhomogeneity along the wall-thickness of Mg alloy CPLIRs is dominated by differences in strain and strain rate between the cylindrical wall and inner rib. Hot flow forming (HFF) is a promising forming technology to manufacture thin-walled cylindrical part with longitudinal inner ribs (CPLIRs) made of magnesium (Mg) alloys, which has wide applications in the aerospace field. However, due to the thermo-mechanical coupling effect and the existence of stiffened structure, complex microstructure evolution and uneven microstructure occur easily at the cylindrical wall (CW) and inner rib (IR) of Mg alloy thin-walled CPLIRs during the HFF. In this paper, a modified cellular automaton (CA) model of Mg alloy considering the effects of deformation conditions on material parameters was developed using the artificial neural network (ANN) method. It is found that the ANN-modified CA model exhibits better predictability for the microstructure of hot deformation than the conventional CA model. Furthermore, the microstructure evolution of ZK61 alloy CPLIRs during the HFF was analyzed by coupling the modified CA model and finite element analysis (FEA). The results show that compared with the microstructure at the same layer of the IR, more refined grains and less sufficient DRX resulted from larger strain and strain rate occur at that of the CW; various differences of strain and strain rate in the wall-thickness exist between the CW and IR, which leads to the inhomogeneity of microstructure rising firstly and declining from the inside layer to outside layer; the obtained Hall-Petch relationship between the measured microhardness and predicted grain sizes at the CW and the IR indicates the reliability of the coupled FEA-CA simulation results. [ABSTRACT FROM AUTHOR]

The impacts of merging on mixed traffic flow in the highway on-ramp zone are numerically investigated in this paper. An on-ramp mixed traffic flow merging model is proposed. Our model focuses on the on-ramp merging zone and considers a mixed traffic flow comprising of connected and automated vehicles (CAVs) and human-driven vehicles (HDVs). Firstly, we establish the Velocity-Modified Comfortable Driving (V-MCD) model for HDVs, which incorporates a velocity estimation module into the base Modified Comfortable Driving (MCD) model. The Cooperative Adaptive Cruise Control (CACC) model developed by PATH Labs is used for CAVs. A cooperative merging model has been developed to capture the interaction behavior of vehicles in various driving scenarios. Merging rules are established based on vehicle type and merging order. The merging rules for HDV-HDV are based on safety gap. Meanwhile, those for CAV-HDV are based on velocity difference, and for CAV-CAV are based on first-come-first-served. We conduct numerical simulation experiments to derive the fundamental diagram of the mixed flow and analyze the interaction between vehicles on the on-ramp and mainline. The simulation results indicate that the V-MCD model can effectively reflect on the hysteresis effect caused by on-ramp merging vehicles in real traffic scenarios. The increase in CAV penetration improves road traffic efficiency in terms of both traffic velocity and capacity. However, as the penetration of CAVs continues to rise, their positive impact will diminish. The sensitivity analysis of the hysteresis effect at both micro and macro levels can enhance our understanding of the impacts on traffic flow. As the hysteresis effect increases, merging has a greater impact on mainline upstream traffic, leading to reduce headway and more erratic velocity changes. [ABSTRACT FROM AUTHOR]

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The object of research is the processes of planning the minimum operating costs of a vessel with minimal risk to it and its cargo, considering the forecasted hydrometeorological conditions. The aim is to increase the fuel efficiency of a vessel’s passage, considering the forecast of weather conditions when forming an optimal safe route in the e-Navigation system. To achieve the research goal, conventional cellular automata and the mathematical apparatus of fuzzy sets and fuzzy logic were used in the process of decision-making and assessment of the impact of weather conditions on traffic efficiency. The devised approach makes it possible to synthesize an optimal route for the vessel, which ensures minimum fuel consumption and has minimal risk for the vessel and cargo while considering variable hydrometeorological conditions along the route. Minimization of operating costs is achieved through the ability of cellular automata to describe the complex behavior of objects, considering local rules. Automata are a computing system in discrete spaces. Data uncertainty has led to the need to use a fuzzy system, the effectiveness of which depends on the quality and accuracy of rules. Fuzzy automata, by combining fuzzy logic and automata theory, made it possible to process continuous steps and model the inherent uncertainty. To determine the state of cells of a fuzzy cellular automaton and the transition function between them, a system of productive rules and membership functions was used. It is the consistency of the system of productive rules when using fuzzy logic to build a cellular automaton that enables the construction of a quasiglobal optimal routing method in comparison with conventional methods for calculating the ship’s route. [ABSTRACT FROM AUTHOR]

Predicting landslide hazards benefits geological disaster prevention and control. A novel cellular automaton (CA) integrating spatial case-based reasoning (SCBR), namely SCBR-CA, is proposed in this paper to predict landslide hazards at a local scale. The proposed model not only extracts spatial scene features for computations but also achieves dynamic prediction, which means that only one input is needed to obtain continuous predictions. Experiments were performed in Lushan, Sichuan, China. After using a convolutional neural network (CNN) to obtain the initial static landslide hazard zoning results, the landslide hazard zoning results for 2016–2025 were predicted with the SCBR-CA model. For comparison, a CA combined with a CNN (CNN-CA), was introduced. The area under the curve (AUC) of the receiver operating characteristic curve and Moran's I index were used to assess the performance of the model. The experimental results showed that SCBR-CA yields slightly better AUC and Moran's I index values than CNN-CA, and the dynamically predicted landslide hazard zoning results are equivalent or superior to those of static zoning, which indicates that the SCBR-CA model effectively predict local landslide hazards. [ABSTRACT FROM AUTHOR]

In this paper, we simulate the hybrid pedestrian movement considering both operational and tactical levels. The video data of our pedestrian route choice experiments are used for validations. Based on the CA model proposed by Nowak and Schadschneider, we build a new modeling framework and introduce six new parameters. Their values are determined by sensitivity analysis. To consider the influence of five statistical results in the simulations, including the velocities and densities of two routes, and the proportion of choosing the longer route, we propose a new metric named OPE (Overall Percentage Error). In order to reduce OPE, four models with different configurations are discussed and compared. We find that the use of shorter time step, modified SFF and the two-stage decision can help to improve the model performance. The simulation results in some other experimental run also shows the validity and universality of the model. In addition, we also compare the outputs of some typical pedestrian simulation software (e.g., AnyLogic), and we find our model has better results. • A hybrid pedestrian model which combines operational and tactical level is discussed. • A floor field cellular automaton model with two-level framework is proposed. • The data from pedestrian route choice experiments are used for validations. • A new indicator named OPE is proposed for evaluating the model performance. • The comparison shows that the model is better than current commercial software. [ABSTRACT FROM AUTHOR]

Staircase choice is one of the most critical factors leading to the difference in pedestrian flow and evacuation routes in buildings with multiple staircases. Neither the shortest path to the building exit nor the locally quickest path to the nearest staircase can represent the natural mode of evacuation path choices for an authentic evacuation simulation. Thus, a prediction-based approach is established to predict and simulate evacuation choices, which helps to address three key issues: (1) extracting evacuation data through a controlled experiment; (2) establishing a Logit model for staircase choice prediction based on experimental data; (3) developing a prediction-based cellular automaton model. The proposed approach has achieved the coupling between choice prediction and evacuation simulation. A comparison with Pathfinder software is conducted to reveal the superiority of the prediction-based CA model for simulating staircase choice. [ABSTRACT FROM AUTHOR]

Hot flow forming (HFF) is a promising forming technology to manufacture thin-walled cylindrical part with longitudinal inner ribs (CPLIRs) made of magnesium (Mg) alloys, which has wide applications in the aerospace field. However, due to the thermo-mechanical coupling effect and the existence of stiffened structure, complex microstructure evolution and uneven microstructure occur easily at the cylindrical wall (CW) and inner rib (IR) of Mg alloy thin-walled CPLIRs during the HFF. In this paper, a modified cellular automaton (CA) model of Mg alloy considering the effects of deformation conditions on material parameters was developed using the artificial neural network (ANN) method. It is found that the ANN-modified CA model exhibits better predictability for the microstructure of hot deformation than the conventional CA model. Furthermore, the microstructure evolution of ZK61 alloy CPLIRs during the HFF was analyzed by coupling the modified CA model and finite element analysis (FEA). The results show that compared with the microstructure at the same layer of the IR, more refined grains and less sufficient DRX resulted from larger strain and strain rate occur at that of the CW; various differences of strain and strain rate in the wall-thickness exist between the CW and IR, which leads to the inhomogeneity of microstructure rising firstly and declining from the inside layer to outside layer; the obtained Hall-Petch relationship between the measured microhardness and predicted grain sizes at the CW and the IR indicates the reliability of the coupled FEA-CA simulation results.

With the growing size of cities and the need to renew residential areas, architects are calling for more efficient use of already settled areas. This paper presents a performance-driven architectural design (PDAD) workflow for shape generation and genetic optimization based on environmental data, using public housing in the Singapore region as a case study. It integrates three-dimensional cellular automata, parametric performance simulation, genetic optimization algorithms, and hierarchical clustering algorithms. The results show that the average value of Useful Daylight Illuminance (UDI) is 85.19%, the average value of Energy Use Intensity (EUI) is 159.41 kWh/m2, and the average value of Predicted Mean Vote (PMV) is 0.64 for the optimal set of solutions produced after genetic optimization. The optimal solution set was further classified into 4 categories by a hierarchical clustering algorithm and was visualized for further evaluation and selection by the architect. The study helps architects to integrate data analysis results with human decision-making as a design research method in the early stages of design and leads to further discussion on bottom-up design approaches in the urban renewal process.

When using a cellular automaton (CA) as a fractal generator, consider orbits from the single site seed, an initial configuration that gives only a single cell a positive value. In the case of a two-state CA, since the possible states of each cell are 0 or 1, the "seed" in the single site seed is uniquely determined to be the state 1. However, for a CA with three or more states, there are multiple candidates for the seed. For example, for a 3-state CA, the possible states of each cell are 0, 1, and 2, so the candidates for the seed are 1 and 2. For a 4-state CA, the possible states of each cell are 0, 1, 2, and 3, so the candidates for the seed are 1, 2, and 3. Thus, as the number of possible states of a CA increases, the number of seed candidates also increases. In this paper, we prove that for linear CAs it is sufficient to consider only the orbit from the single site seed with the seed 1. • Sufficient to consider only orbits where the seed of linear cellular automata is 1. • When the number of states is prime, orbits are isomorphic regardless of seed. • When the number is composite, there is an orbit that has seed 1 and is isomorphic. [ABSTRACT FROM AUTHOR]

Descriptive complexity provides intrinsic, i.e. machine-independent , characterizations of the main complexity classes. On the other hand, logic can be useful for designing programs in a natural declarative way. This is especially important for parallel computation models such as cellular automata, since designing parallel programs is considered a difficult task. This paper establishes three logical characterizations of the three classical complexity classes modeling minimal time, called real-time , of one-dimensional cellular automata according to their canonical variations: unidirectional or bidirectional communication, input word given in a parallel or sequential way. Our three logics are natural restrictions of existential second-order Horn logic with built-in successor and predecessor functions. These logics correspond exactly to the three ways of deciding a language on a square grid circuit of side n according to one of the three natural locations of an input word of length n : along a side of the grid, on the diagonal that contains the output cell – placed on the vertex (n,n) of the square grid–, or on the diagonal opposite to the output cell. The key ingredient to our results is a normalization method that transforms a formula from one of our three logics into an equivalent normalized formula that closely mimics a grid circuit. Then, we extend our logics by allowing a limited use of negation on hypotheses like in Stratified Datalog. By revisiting in detail a number of representative classical problems - recognition of the set of primes by Fisher's algorithm, Dyck language recognition, Firing Squad Synchronization problem, etc. - we show that this extension makes easier programming and we prove that it does not change the real-time complexity of our logics. Finally, based on our experience in expressing these representative problems in logic, we argue that our logics are high-level programming languages: they make it possible to express in a natural, complete and synthetic way the algorithms of the literature, based on signals – and even to design new inductive algorithms –, and to translate them automatically into cellular automata of the same complexity. [ABSTRACT FROM AUTHOR]

Land use and land cover change (LUCC) modeling is crucial to urban planning and policy making. A well-used and effective paradigm for LUCC is the ANN-CA model which employs an artificial neural network (ANN) to calculate a transition probability over each land cell from various driving factors, and then uses a cellular automaton (CA) to evolve all cells consecutively to update their land usage and coverage according to the estimated probability distribution. This paper focuses on the effect of delays or perturbations possibly taking place between land cells on the LUCC modeling. To this end, a new ANN-CA model is proposed which adopts an asynchronous communicating cellular automaton (ACCA), rather than the conventional synchronous CA. Especially, the ACCA allows every cell to communicate with its neighbors independently at random times via a specific protocol, which offers a natural way to include stochastic delays in exchanging the current land usages between cells. As a result, every change of a cell's land use in the ACCA may not affect its neighbors immediately, but is subject to delays that might play an important role in modeling the practical LUCC. Numerical analysis of the new model are carried out over three regions of Chongqing city, China with different scales: Yongchuan District, Sanjiao Town, and Huangguashan Village, and experimental results demonstrate that the proposed ANN-ACCA model can achieve a higher accuracy for LUCC simulation as compared to conventional ANN-CA models. [ABSTRACT FROM AUTHOR]

Compared to the heterogeneous traffic flow on roads, the heterogeneous characteristics of maritime traffic flow are more pronounced, due to disparities in the manoeuvrability, size, and safety requirements among different ships. These factors increase the complexity of quantifying traffic efficiency. This paper employs hierarchical clustering to categorise trajectories with similar speed variation features and utilises Long Short-Term Memory (LSTM) models to predict ship speeds, forming a speed control strategy based on time-series data. Moreover, extending from the principles of car-following, models are developed to compute dynamic safety distances for both manned and autonomous ships. Further, a port waterway simulation model based on cellular automaton (CA) is developed, integrating data-driven speed control strategies while maintaining dynamic safety distances, resulting in a comprehensive simulation model with dual speed control mechanisms. A case study of the Tianjin port shows the advantages of dynamic safety distances. Dynamic safety distances significantly improved ship navigation and overall channel traffic efficiency. The inclusion of autonomous ships further improves the efficiency and the benefits are directly related to the proportion of autonomous ships. This research provides new insights and methodologies for assessing transport efficiency and waterway capacity, which also offers support for research on autonomous maritime traffic flow. • By using dynamic time warping and hierarchical clustering, ship trajectories were categorised based on speed variations. • A Long Short-Term Memory (LSTM) model clarified ship speed changes, enriching navigational pattern analysis. • One model was proposed to calculate dynamic safety distances for both manned and autonomous ships. • A cellular automaton model was developed with two key modules: ship speed control and dynamic ship safety distance. • An empirical case study of the main channel of Tianjin harbour showed the advantages of the proposed approaches. [ABSTRACT FROM AUTHOR]

Science is currently becoming aware of the challenges in the understanding of the very root mechanisms of massively parallel computations that are observed in literally all scientific disciplines, ranging from cosmology to physics, chemistry, biochemistry, and biology. This leads us to the main motivation and simultaneously to the central thesis of this review: "Can we design artificial, massively parallel, self-organized, emergent, error-resilient computational environments?" The thesis is solely studied on cellular automata. Initially, an overview of the basic building blocks enabling us to reach this end goal is provided. Important information dealing with this topic is reviewed along with highly expressive animations generated by the open-source, Python, cellular automata software GoL-N24. A large number of simulations along with examples and counter-examples, finalized by a list of the future directions, are giving hints and partial answers to the main thesis. Together, these pose the crucial question of whether there is something deeper beyond the Turing machine theoretical description of massively parallel computing. The perspective, future directions, including applications in robotics and biology of this research, are discussed in the light of known information. [ABSTRACT FROM AUTHOR]

The latest advances in additive manufacturing have given rise to an increasing interest in additively built lattice structures due to their superior properties compared to foams and honeycombs. The foundation of these superior properties is a tailored microstructure, which is difficult to achieve in additive manufacturing because of the variety of process parameters influencing the quality of the final part. This work presents the numerical prediction of the resulting grain structure of a lattice structure additively built by electron beam powder bed fusion. A thermal finite-difference model is coupled to a sophisticated cellular automaton-based crystal growth model, including nucleation. Numerically predicted grain structures, considering different nucleation conditions, are compared with experimentally derived EBSD measurements. The comparison reveals that nucleation is important, especially in fine lattice structures. The developed software, utilizing the nucleation model, is finally able to predict the as-built grain structure in lattice structures. [ABSTRACT FROM AUTHOR]

• A full-period fringe order correction approach based on dual-threshold cellular automaton is proposed. • A sequential segmentation algorithm is proposed to segment independent connected domains. • The proposed method allows for the measurement of objects with steep height variations. In traditional temporal phase unwrapping (TPU) methods, the fringe order is obtained pixel-to-pixel by multi-frequencies or multi-wavelengths. The direct calculation and error non-accumulation features accelerate the prosperity of TPU. Nevertheless, the noise, defocusing, and non-uniform reflectivity may inevitably lead to some fringe order errors. These errors are powerless against the evolving TPUs such as Gray code and phase coding. In this paper, a full-period fringe order correction method based on dual-threshold cellular automaton is proposed for machine 3D vision. Initially, an advanced dual-threshold cellular automaton algorithm is employed to extract both the strong and weak edges of the wrapped phase individually. Superior to conventional single-threshold edge detection methods, this approach effectively mitigates the edge breakage problem caused by significant height variations. Subsequently, the N-filled map, N-residue mask, and N-start points concepts are introduced to sequentially segment independent connected domains based on the tightly graphical coupling. In addition, by performing edge compensation in the same period, accurate fringe order correction can be achieved even if excessive edge points are identified, as long as the broken edges are effectively connected. The experimental results exhibit exceptional correction performance of the proposed method for intricate isolated objects, objects with non-uniform reflectivity, and dynamic scenes. [ABSTRACT FROM AUTHOR]

The abnormal grain growth of steel, which is occurs during carburization, adversely affects properties such as heat treatment deformation and fatigue strength. This study aimed to control abnormal grain growth by controlling the materials and processes. Thus, it was necessary to investigate the effects of microstructure, precipitation, and heat treatment conditions on abnormal grain growth. We simulated abnormal grain growth using the cellular automaton (CA) method. The simulations focused on the grain boundary anisotropy and dispersion of precipitates. We considered the effect of grain boundary misorientation on boundary energy and mobility. The dispersion state of the precipitates and its pinning effect were considered, and grain growth simulations were performed. The results showed that the CA simulation reproduced abnormal grain growth by emphasizing the grain boundary mobility and the influence of the dispersion state of the precipitate on the occurrence of abnormal grain growth. The study findings show that the CA method is a potential technique for the prediction of abnormal grain growth. [ABSTRACT FROM AUTHOR]

The exploration of the relationship between process parameters and grain evolution during the thermal deformation of rare-earth magnesium alloys using simulation software has significant implications for enhancing research and development efficiency and advancing the large-scale engineering application of high-performance rare-earth magnesium alloys. Through single-pass hot compression experiments, this study obtained high-temperature flow stress curves for rare-earth magnesium alloys, analyzing the variation patterns of these curves and the softening mechanism of the materials. Drawing on physical metallurgical theories, such as the evolution of dislocation density during dynamic recrystallization, recrystallization nucleation, and grain growth, the authors of this paper establish a cellular automaton model to simulate the dynamic recrystallization process by tracking the sole internal variable—the evolution of dislocation density within cells. This model was developed through the secondary development of the DEFORM-3D finite element software. The results indicate that the model established in this study accurately simulates the evolution process of grain growth during heat treatment and the dynamic recrystallization microstructure during the thermal deformation of rare-earth magnesium alloys. The simulated results align well with relevant theories and metallographic experimental results, enabling the simulation of the dynamic recrystallization microstructure and grain size prediction during the deformation process of rare-earth magnesium alloys.