Cellular Automata: Analysis And Applications
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This book provides an overview of the main approaches used to analyze the dynamics of cellular automata. Cellular automata are an indispensable tool in mathematical modeling. In contrast to classical modeling approaches like partial differential equations, cellular automata are relatively easy to simulate but difficult to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction to cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of various topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification) These classifications suggest that cellular automata be clustered, similar to the classification of partial differential equations into hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question of whether the properties of cellular automata are decidable. Surjectivity and injectivity are examined, and the seminal Garden of Eden theorems are discussed. In turn, the third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows us to define self-similar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit). Pattern formation is related to linear cellular automata, to the Bar-Yam model for the Turing pattern, and Greenberg-Hastings automata for excitable media. In addition, models for sand piles, the dynamics of infectious d
These definitions are qualitative in nature and there is some room for interpretation. According to Wolfram, \"...with almost any general classification scheme there are inevitably cases which get assigned to one class by one definition and another class by another definition. And so it is with cellular automata: there are occasionally rules...that show some features of one class and some of another.\" Wolfram's classification has been empirically matched to a clustering of the compressed lengths of the outputs of cellular automata.
In this paper, the cellular automaton simulation technology is applied to the evacuation management of sports events, combined with the dynamic analysis method to analyze the collision of people in the evacuation process. At the same time, the cellular automaton model is used to refine the evacuation space to simplify environmental modeling, and the network model is used to determine the individual evacuation path from a macroperspective, simplify modeling, and improve simulation efficiency. In addition, this article simulates the evacuation process of the cellular automaton according to the actual evacuation situation of sports events and constructs the evacuation management system of sports events. Finally, this article evaluates the effect of the model in conjunction with experiments. The experimental results show that the role of the evacuation management system for sports events based on cellular automata proposed in this paper is obvious.
This paper applies dynamic analysis to the evacuation management process of sports events and simulates the evacuation process of sports events through cellular automata to improve the evacuation management effect of sports events.
The dynamic analysis model of this paper is studied through experimental research, and the performance effect of the cellular automata in the dynamic analysis model is statistically evaluated by the expert evaluation method, and the results shown in Table 2 below are obtained.
It can be seen from Table 2 that the cellular automata perform very well in the dynamic analysis model. On the basis of the above research, the evacuation management system of sports events based on the cellular automata constructed in this paper is evaluated, and the evaluation results are shown in Table 3 below.
From the experimental analysis, it can be seen that the evacuation management system for sports events based on the cellular automata proposed in this paper can play an important role in the evacuation of sports events.
In the study of evacuation of stadium personnel, it is necessary to study the evacuation characteristics of stadiums as well as the characteristics of individual personnel in evacuation situations. The research on the virtual exercise of stadium personnel evacuation includes the above two research aspects, which can provide an effective research approach for the evacuation of stadium personnel and even other venues. Therefore, the research on the virtual exercise system for evacuation of stadiums can not only provide a basis for determining the rationality of stadium construction but also provide a basis for the formulation of evacuation plans. This paper applies dynamic analysis to the evacuation management process of sports events and simulates the evacuation process of sports events through cellular automata to improve the evacuation management effect of sports events. The experimental research results show that the evacuation management system for sports events based on cellular automata proposed in this paper can play an important role in the evacuation of sports events.
Any digital image also considers regular grid of cells called pixels and henceforth cellular automata is performed for image processing for the edge detection in digital image. Edge detection methods based on Cellular Automata has major advantages over conventional approaches because it is computationally effective, and may be utilized for particular applications by choosing suitable rules. Various CA based edge detection approaches are implemented and tested for enabling a primary comparison between existing approaches.
Abstract:The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and the large number of biological components involved make the modeling and the analysis of electrophysiological properties in cardiac tissue still an open challenge. We consider here a Hybrid Cellular Automata (HCA) approach modeling the cardiac cell-cell membrane resistance with a free variable. We show that the modeling approach can reproduce important and complex spatiotemporal properties paving the ground for promising future applications. We show how GPU-based technology can considerably accelerate the simulation and the analysis. Furthermore, we study the cardiac behavior within a unidimensional domain considering inhomogeneous resistance and we perform a Monte Carlo analysis to evaluate our approach.Keywords: Cellular Automata; cardiac modeling; Monte Carlo simulation; matlab simulink; GPU
Abstract:Rapid urban growth has historically led to changes in land use patterns and the degradation of natural resources and the urban environment. Uncontrolled growth of urban areas in the city of Quito has continued to the present day since 1960s, aggravated by illegal or irregular new settlements. The main objective of this paper is to generate spatial predictions of these types of urban settlements and land use changes in 2023, 2028 and 2038, applying the Dinamica EGO cellular automata and multivariable software. The study area was the Machachi Valley between the south of the city of Quito and the rural localities of Alóag and Machachi. The results demonstrate the accuracy of the model and its applicability, thanks to the use of 15 social, physical and climate predictors and the validation process. The analysis of the land use changes throughout the study area shows that urban land use will undergo the greatest net increase. Growth in the south of Quito is predicted to increase by as much as 35% between 2018 and 2038 where new highly vulnerable urban settlements can appear. Native forests in the Andes and forest plantations are expected to decline in the study area due to their substitution by shrub vegetation or agriculture and livestock land use. The implementation of policies to control the land market and protect natural areas could help to mitigate the continuous deterioration of urban and forest areas.Keywords: land use change; cellular automata; Quito; native forest; urban land use; rural land use
A cellular automaton (CA) is a collection of cells arranged in a grid of specified shape, such that each cell changes state as a function of time, according to a defined set of rules driven by the states of neighboring cells. CAs have been suggested for possible use in public key cryptography, as well as for applications in geography, anthropology, political science, sociology and physics, among others.
On the other hand, several models have been introduced to study the collective movement of particles and cells35,36,37. Cellular automata (CA) in particular have the advantage of being less computationally demanding than continuous models when performing simulations. A specific type of CA is the so-called lattice-gas cellular automata (LGCA)38. In LGCA, each lattice node can contain several particles, which at each time step are rearranged within the lattice node according to the interaction rule, and subsequently moved to a neighboring node. In a biological context particles can be regarded as cells, while the LGCA rules mimic cell migration and interaction. Furthermore, LGCA have proved to be amenable to mathematical analysis39. For this reason, LGCA have been introduced as mesoscopic models for single and collective cell migration40,41,42,43. So far, none of the mentioned models has considered anomalous migration of single cells. 59ce067264