Conventional Cellular Automata Research Articles

Modeling urban growth with GIS based cellular automata and least squares SVM rules: a case study in Qingpu–Songjiang area of Shanghai, China

A critical issue in urban cellular automata (CA) modeling concerns the identification of transition rules that generate realistic urban land use patterns. Recent studies have demonstrated that linear methods cannot sufficiently delineate the extraordinary complex boundaries between urban and non-urban areas and as most urban CA models simulate transitions across these boundaries, there is an urgent need for good methods to facilitate such delineations. This paper presents a machine learning CA model (termed MachCA) with nonlinear transition rules based on least squares support vector machines (LS-SVM) to simulate such urban growth. By projecting the input dataset into a high dimensional space using the LS-SVM method, an optimal hyper-plane is constructed to separate the complex boundaries between urban and nonurban land, thus enabling the retrieval of nonlinear CA transition rules. In the MachCA model, the transition rules are yes–no decisions on whether a cell changes its state or not, the rules being dynamically updated for each iteration of the model implementation. The application of the MachCA for simulating urban growth in the Shanghai Qingpu–Songjiang area in China reveals that the spatial configurations of rural–urban patterns can be modeled. A comparison of the MachCA model with a conventional CA model fitted by logarithmic regression (termed LogCA) shows that the MachCA model produces more hits and less misses and false alarms due to its capability for capturing the spatial complexity of urban dynamics. This results in improved simulation accuracies, although with only less than 1 % deviation between the overall errors produced by the MachCA and LogCA models. Nevertheless, the way MachCA model use in retrieving the transition rules provides a new method for simulating the dynamic process of urban growth.

Fuzzy Cellular Automata Models for Crowd Movement Dynamics at Signalized Pedestrian Crossings

Crowd movement dynamics at a signalized pedestrian crossing constitutes a complex system affected by many factors. Existing crowd simulation models seldom consider cognition and decision making of individual pedestrians. In this study, a fuzzy cellular automata (FCA) model was developed to simulate pedestrian movements at crowded signalized pedestrian crossings that incorporated pedestrian decision-making processes. The proposed FCA model incorporated fuzzy logic into a conventional cellular automata (CA) model. In contrast to existing models and applications, the proposed FCA model used fuzzy sets and membership functions to simulate individuals’ decision making process. Four fuzzy sets were applied for each decision: stop or go (stop–go) decision, moving direction, velocity change, and congregation. Membership functions of each input factor as well as weight factors of each fuzzy set at different movement zones were calibrated on the basis of field observations. Model performance was assessed by comparisons of trajectories between estimation and observation, interactions with conflicting vehicles and pedestrians, and congregation phenomena. Through a simulation experiment and comparison with existing approaches, simulation results show that the FCA model can well replicate crowd movement dynamics in real-world pedestrian crossings.

A Cellular Automata Model Based on Nonlinear Kernel Principal Component Analysis for Urban Growth Simulation

In this paper we present a cellular automata (CA) model based on nonlinear kernel principal component analysis (KPCA) to simulate the spatiotemporal process of urban growth. As a generalisation of the linear principal component analysis (PCA) method, the KPCA method was developed to extract the nonspatially correlated principal components amongst the various spatial variables which affect urban growth in high-dimensional feature space. Compared with the linear PCA method, the KPCA approach is superior as it generates fewer independent components while still maintaining its capacity to reduce the noise level of the original input datasets. The reduced number of independent components can be used to better reconstruct the nonlinear transition rules of a CA model. In addition, the principal components extracted through the KPCA approach are not linearly related to the input spatial variables, which accords well with the nonlinear nature of complex urban systems. The KPCA-based CA model (KPCA-CA) developed was fitted to a fast-growing region in China's Shanghai Metropolis for the sixteen-year period 1992–2008. The simulated patterns of urban growth matched well with the observed urban growth, as determined from historical remotely sensed images for the same period. The KPCA-CA model resulted in significant improvements in locational accuracy when compared with conventional CA models and acted to reduce simulation uncertainty.

On Cellular Automata rules of molecular arrays

Cellular Automata (CA) have long attracted interest as abstract computation models, but only in the last few years have serious attempts started to implement them in terms of molecules. Such nano-technological innovations promise very cost-effective fabrication because of the regular structure of CA, which allows assembly through molecular self-organization. The small sizes of molecules combined with their availability in Avogadro-scale numbers promises a huge computational power, in which the massive parallelism inherent in CA can be effectively exploited. This paper discusses the molecular CA in (Bandyopadhyay et al., Nature Physics 2010) and shows novel features that have never been proposed in conventional CA models. The interaction rules in the molecular CA are found to be of a mixed variety, ranging from conventional direct-neighborhood type of rules to rules with long-distance interactions between cells. The probabilities according to which rules are applied in the molecular CA are dynamically influenced by the patterns on the cellular space. This results in extremely rich behavior, as compared to conventional models, which has the potential to be utilized for efficient configuration of patterns on the cellular space.

Numerical modeling of dynamic recrystallization during nonisothermal hot compression by cellular automata and finite element analysis

In this study, dynamic recrystallization during nonisothermal hot compression was numerically simulated by cellular automata and finite element analysis. A modified cellular automata model was developed by introducing a new parameter for considering solute drag effect. The isothermal hot compression tests of pure copper were carried out to verify the modified cellular automata model by comparing material behavior and average grain size. The effect of solute drag was numerically considered and compared to the experimental data and the numerical data obtained by conventional cellular automata without solute drag effect. Then, the modified cellular automata model was applied to a nonisothermal hot compression by combining with a finite element analysis. The finite element analysis was conducted to acquire local parameters such as strain, strain rate, and temperature. These values were provided to the cellular automata model as input. The local changes of microstructure and average grain size were simulated by cellular automata and compared with nonisothermal hot compression results. The simulation results were in reasonably good agreement with experimentally determined microstructures by electron backscattering diffraction. The developed model was further applied to simulate a hot gear blank forging process to check its applicability. With the current approach, local microstructures can be determined for better understanding microstructural changes during the nonisothermal process.

A very effective density classifier two-dimensional cellular automaton with memory

Conventional cellular automata (CA) are memoryless, i.e. the new state of a cell depends on the neighborhood configuration solely at the preceding time step. This paper considers an extension to the standard framework of CA by implementing memory capability in cells. It is shown that the HPP rule, one of the most important block automaton rules, endowed with the memory of the most frequent recent state, behaves as an excellent classifier of the density in the initial configuration, which surpasses the performance of the best two-dimensional density classifier reported in the literature.

Complex Dynamics Emerging in Rule 30 with Majority Memory

In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and show that using the memory function we can transform quasi-chaotic dynamics of classical Rule 30 into domains of travelling structures with predictable behaviour. We analyse morphological complexity of the automata and classify dynamics of gliders (particle, self-localizations) in memory-enriched Rule 30. We provide formal ways of encoding and classifying glider dynamics using de Bruijn diagrams, soliton reactions and quasi-chemical representations.

A structurally dynamic cellular automaton with memory

Abstract Major features of conventional cellular automata (CA) include the inalterability of topology and the absence of memory. The effect of simple memory (memory in cells and links) in a particular structurally dynamic CA is explored in this paper.

Fuzzy Cellular Automata for Modeling Pattern Classifier

This paper investigates the application of the computational model of Cellular Automata (CA) for pattern classification of real valued data. A special class of CA referred to as Fuzzy CA (FCA) is employed to design the pattern classifier. It is a natural extension of conventional CA, which operates on binary string employing boolean logic as next state function of a cell. By contrast, FCA employs fuzzy logic suitable for modeling real valued functions. A matrix algebraic formulation has been proposed for analysis and synthesis of FCA. An efficient formulation of Genetic Algorithm (GA) is reported for evolution of desired FCA to be employed as a classifier of datasets having attributes expressed as real numbers. Extensive experimental results confirm the scalability of the proposed FCA based classifier to handle large volume of datasets irrespective of the number of classes, tuples, and attributes. Excellent classification accuracy has established the FCA based pattern classifier as an efficient and cost-effective solutions for the classification problem.

Random grid, three-dimensional, space-time coupled cellular automata for the simulation of recrystallization and grain growth

A new three-dimensional, random grid based cellular automaton model for the simulation of the evolution of a materials microstructure during recrystallization and grain growth is presented. The paper describes how the model can be linked to space and time coordinates and illustrates how theoretical analytical models describing grain boundary motion under the influence of a driving force can be used to control the cellular automaton. Simulation experiments illustrate the random grid base of the automaton eliminates the dependence of the model on the grid symmetry as observed in conventional cellular automata. Examples illustrating the correctness of the approach and its implementation are presented in the form of different verification experiments, including growth kinetics of a two different theoretical recrystallization processes, the shrinkage of a spherical grain driven by the curvature of its boundary and the evolution of the grain size distribution during grain growth in a polycrystalline microstructure.

グラフオートマタ

A variety of models of self-reproduction process have been proposed since von Neumann initiated this field. Almost all of them are described within the framework of two-dimensional cellular automata. They are heavily dependent on or limited by the peculiar properties of the two dimensional lattice spaces, but such properties are irrelevant to the essential nature of self-reproduction. In this paper, we introduce a new framework called “graph automata” to obtain a natural description of complicated spatio-temporal developmental processes. As an illustrative example, a self-reproduction of Turing machine, which requires very long description by conventional cellular automata, is shown in a simple and straightforward formulation.

Graph automata: natural expression of self-reproduction

A variety of models of self-reproduction process have been proposed since von Neumann initiated this field with his self-reproducing automata. Almost all of them are described within the framework of two-dimensional cellular automata. They are heavily dependent on or limited by the peculiar properties of the two-dimensional lattice spaces. But such properties are irrelevant to the essential nature of self-replication. In this paper, we introduce a new framework called “graph automata” to obtain a natural description of complicated spatio-temporal developmental processes such as self-reproduction. The most advantageous point of this methodology is that it is not restricted to particular lattice space. As an illustrative example, a self-reproduction of Turing machine, which requires very long description by conventional cellular automata, is shown in a simple and straightforward formulation. Graph automata provide a new tool to approach important scientific problems such as evolution of morphology, and also to give the basis of self-reproducing and self-repairing artifacts.

Neural-network-based cellular automata for simulating multiple land use changes using GIS

This paper presents a new method to simulate the evolution of multiple land uses based on the integration of neural networks and cellular automata using GIS. Simulation of multiple land use changes using cellular automata (CA) is difficult because numerous spatial variables and parameters have to be utilized. Conventional CA models have problems in defining simulation parameter values, transition rules and model structures. In this paper, a three-layer neural network with multiple output neurons is designed to calculate conversion probabilities for competing multiple land uses. The model involves iterative looping of the neural network to simulate gradual land use conversion processes. Spatial variables are not deterministic because they are dynamically updated at the end of each loop. A GIS is used to obtain site attributes and training data, and to provide spatial functions for constructing the neural network. The parameter values for modelling are automatically generated by the training procedure of neural networks. The model has been successfully applied to the simulation of multiple land use changes in a fast growing area in southern China.

An interpolated flux scheme for cellular automaton device simulation

Cellular automaton (CA)-based device simulation is one of the most powerful tool to solve Boltzmann transport equation (BTE) of carriers in semiconductor devices. In comparison to the Monte Carlo (MC) method which suffers statistical noise problems, cell representation used in the CA method realizes noise free analysis of the carrier distribution function (DF) both in real and momentum space. However, CA requires more computer resources than MC in typical cases because cell sizes used for both real and momentum space are restricted to be small enough not to cause artificial diffusion (ADF). In this paper, a new scheme for calculation of flux among cells is proposed in which carrier distribution is interpolated between neighbor cells. The suppression of ADF is confirmed through comparisons to other simulation methods in homogeneous cases, an n/sup +/-p diode case and an n/sup +/-n-n/sup +/ structure case. Consistency with MC analysis is also demonstrated by analyzes of homogeneous cases and an n/sup +/-n-n/sup +/ case and also by a theoretical study. A speed up of at least two orders of magnitude can be obtained by introducing the new flux calculation whose accuracy is ensured with much less number of cells than conventional CA methods. Consequently, this CA method is drastically improved as a practical tool for semiconductor device modeling from the point of CPU time and accuracy.

Adaptive stochastic cellular automata: Theory

The mathematical concept of cellular automata has been generalized to allow for the possibility that the uniform local interaction rules that govern conventional cellular automata are replaced by nonuniform local interaction rules which are drawn from the same probability distribution function, in order to guarantee the statistical homogeneity of the cellular automata system. Adaptation and learning in such a system can be accomplished by evolving the probability distribution function along the steepest descent direction of some objective function in a statistically unbiased way to ensure that the cellular automata's dynamical behavior approaches the desired behavior asymptotically. The proposed CA model has been shown mathematically to possess the requisite convergence property under general conditions.