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Introduction to Modeling of Complex Systems Using Cellular Automata - intro from editors of the book "Simulating Complex Systems by Cellular Automata"



..... The INTRODUCTION into the one of the best selling book in the field (over 30k ebooks sold) ..... Abstract: Since the sixteenth century there have been two main paradigms in the methodology of doing science. The first one is referred to as “the experimental” paradigm. During an experiment we observe, measure, and quantify natural phenomena in order to solve a specific problem, answer a question, or to decide whether a hypothesis is true or false. The second paradigm is known as “the theoretical” paradigm. A theory is generally understood as a fundamental, for instance logical and/or mathematical explanation of an observed natural phenomenon. Theory can be supported or falsified through experimentation. Link to the online version of the book:
Book: Simulating Complex Systems by Cellular Automata
Jiri Kroc, Peter M. A. Sloot, Alfons G. Hoekstra
Springer (book publisher)
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Hopefully, you do find this book useful in your own research. Good luck at your research!
Jiří Kroc, Ph.D.
Faculty of Medicine in Pilsen
Biomedical Center
Alej Svobody 1655/76
323 00 Pilsen Severní Předměstí
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... A concise introduction into cellular automata (CA) [30] along with CA-books covering quite diverse topics & CA-examples [14,29] are (a) No output: empty matrix without any initialized alive cell with a silent, embedded local rule gives empty output. ...
... A recommended, easy to-think-through starting point to understand the very principles of CA-computations and programming is the following, less than one hundred lines long Python program simulating the John. H. Conway's 'Game of Life' [18] along with CA-theory covered, e.g., in [30]. This is recommended to be followed by books [38] and more advanced software [20,19,46]. ...
... (b) The first four breathing ships (a rectangle with two dots above it) occurs, e.g., see coordinates (30,30), step #30. ...
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Scientists are gradually 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, physics, across chemistry, biochemistry, and ending in 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?" A large number of simulations along with examples and counterexamples , finalized by a list of the future directions, are giving hints and partial answers to the main thesis. This all together is opening the crucial question whether there is existing a deeper, beyond the Turing machine theoretical description of massively-parallel computing. Important information dealing with this topic is reviewed along with highly expressive animations generated by the open-source, Python software GoL-N24. The perspective, future directions including applications in robotics and biology of this research are discussed in the light of known information.
... Cellular Automata (CAs) represent a special case of CSs where a space is discretized into a uniform lattice of elements (e.g. squares, triangles, or hexagons in two dimensions or cubes in three dimensions) called cells and where time proceeds in discrete time steps 12,14 . Generally, the values of all variables attached to each process (cell) are changed to their new values according to a uniform governing (also transition, evolution, CAs) rule simultaneously for each new time step. ...
... Complex Systems Systems composed of a large number of locally interacting entities (processes) that are relatively simple, which produce self-organization and emergent behavior 14,76,77 . ...
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This review aims mainly to all professionals from the fields of clinical medicine, biomedical and experimental research. It targets to deliver a quick starting overview and basic understanding of Complex Systems (CSs) with a citation apparatus enabling to efficiently reach the cutting-edge knowledge and applications. This paper has two main objectives. It builds the core information of CSs that is explained on a carefully selected example called the "Game of Life", which expresses self-organization and emergence. The second and most important objective is to provide a wide list of CSs computational methods enabling everybody to achieve a basic overview of all major methods applied in experimental and clinical medicine. These methods are easy to implement in any field of the interest.
... • Physics: Cellular automata have been used to model a wide range of physical systems, including fluid dynamics, magnetohydrodynamics, and solidstate physics. For example, the Ising model is a well-known cellular automaton used to study magnetic materials [18][19][20][21]. ...
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Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for more dynamic and realistic simulations. This thesis explores the design, dynamics, and applications of LCA, with a focus on its potential in pattern recognition and classification. The research begins by introducing the limitations of traditional CA in capturing the complexity of real-world systems. It then presents the concept of LCA, where layer 0 corresponds to a predefined model, and layer 1 represents the proposed model with additional influence. The interlayer rules, denoted as f and g, enable interactions not only from adjacent neighboring cells but also from some far-away neighboring cells, capturing long-range dependencies. The thesis explores various LCA models, including those based on averaging, maximization, minimization, and modified ECA neighborhoods. Additionally, the implementation of LCA on the 2-D cellular automaton Game of Life is discussed, showcasing intriguing patterns and behaviors. Through extensive experiments, the dynamics of different LCA models are analyzed, revealing their sensitivity to rule changes and block size variations. Convergent LCAs, which converge to fixed points from any initial configuration, are identified and used to design a two-class pattern classifier. Comparative evaluations demonstrate the competitive performance of the LCA-based classifier against existing algorithms. Theoretical analysis of LCA properties contributes to a deeper understanding of its computational capabilities and behaviors. The research also suggests potential future directions, such as exploring advanced LCA models, higher-dimensional simulations, and hybrid approaches integrating LCA with other computational models.
... They are made up of a group of units ( cells ) connected in a regular lattice with other units, and subjected to a local function (or rule) that determines the next state of each individual unit, by acting on the current unit's state together with those of its neighbouring cells, i.e., those locally connected to the unit. Cellular automata have been studied both from the point of view of their mathematical and computational properties as well as systems capable of simulating real-world phenomena [3] , such as disease spread [4] , urban growth [5] , fluid dynamics [6] , collective social phenomena [7] , among others. ...
Classically, cellular automata and, in fact, automata networks in general, have synchronous dynamics defined by a local function. But the interest on asynchronous versions of both systems has grown, since it provides an extra degree of freedom. The standard way to define deterministic asynchronism is to set an update priority to each node. It has been shown that these networks can solve problems that were not previously solvable with synchronous systems. However, such a way to define asynchronism depends totally on the relative position of the node in the network. Here, we propose a new way to look at asynchronism in such systems, in that the priority now relies on the state transitions of the system’s underlying local function. This leads to a scalable way to add deterministic asynchronism in such networks. Taking the elementary cellular automata space as a baseline, we carry out a complete characterisation of its dynamics using the proposed asynchronism update scheme.
... A quite sensible point in engineering complex systems is easily stated and yet very hard to implement or work with. The question has to do with how are we to understand the desirable complexity that is to be produced [26,27]. Here more than anywhere else the interplay and positive loops among information, computation and knowledge become fundamental. ...
The local function of cellular automata is usually applied to all cells in the lattice in just one single time step. Such a synchronous update may lead to limitations, as when models for real-world systems are being created. As a counterbalance, asynchronous forms of update have been more and more explored in the literature, as they can provide an extra degree of freedom. The standard way to define deterministic asynchronism by setting an update priority to each cell depends totally on the cell position in the lattice. In a previous work, we proposed a new way to address deterministic asynchronism, where the update priority would rely on the state transitions underlying the local function, in a way that any cell might be updated multiple times during the same iteration. Here, we consider a restricted version of the latter, by which the cells are necessarily updated just once during any time step. By focusing on the elementary cellular automata space, we provide a complete characterisation of the resulting number of distinct dynamics of the entire space, out of all possible independent updates, and contrast it with the case of multiple updates.
The density classification task is one of the most adopted benchmark problems to study computational abilities of cellular automata. It consists in designing a cellular automaton that converges to uniform configurations according to the most frequent state in initial configurations. Earlier solutions for this task were designed by different methods and techniques; but since the symmetry and the number-conserving properties were introduced, many unknown solutions were found. In this work, we are interested in analyzing and understanding the general mechanisms by which cellular automata perform decentralized emergent computations to solve that task. For this purpose, we firstly propose a regular structure for the space of symmetric number-conserving cellular automata rules of radius r = 3. This allows us to outline their supported low-level computations. We show then that the proposed structure can significantly help to analyze the different solutions and, to make comparisons and conceptual connections among them. It also allows giving explanations about the computational strategies used by the currently best-known solutions. Consequently, we could design new higher performing solutions – as compared to the currently best-known ones – using cellular automata of radius r = 4.
Artykuł stanowi podsumowanie badań prowadzonych przez autora w zakresie praktycznego wykorzystania technik symulacji komputerowych w odniesieniu do problematyki nauk społecznych, ze szczególnym uwzględnieniem politologii oraz socjologii. Głównym przedmiotem badań były wielo- agentowe modele symulacyjne (ABM - Agent-Based Models), które znalazły jak dotąd najszersze zastosowanie na gruncie nauk społecznych. Przytoczone przykłady modeli wieloagentowych (model segregacji przestrzennej Schellinga oraz model ewolucji postaw etnocentrycznych Axelroda-Hammonda) oparte zostały na autorskich implementacjach napisanych w języku Python 3.6. Wykorzystano to narzędzie, w celu bezpośredniej weryfikacji ustaleń poczynionych przez cytowanych autorów, a także dokładnego przedstawienia zastosowanej przez nich metodologii. Ujęta w pracy dyskusja obejmuje kwestie związane z prawdziwością modeli symulacyjnych, a co za tym idzie zasadnością ich użycia w celach naukowych.
In this paper we study the influence of spatio-temporal correlations on the dynamic runtime behavior of the optimistic parallel Time Warp simulation method. By means of Ising spin simulation, we show experimentally that the probability distribution of the number of rolled back events behaves as a power-law distribution over a large range of sub-critical Ising temperatures and decays exponentially for super-critical Ising temperatures. The experimental results indicate that for critical Ising temperatures, where long-range correlations occur, the computational complexity of Time Warp and physical complexity of the Ising spin model are entangled and contribute both to the runtime behavior in a nonlinear way.  2001 Elsevier Science B.V. All rights reserved.
We consider flocks of artificial birds and study the emergence of V-like formations during flight. We introduce a small set of fully distributed positioning rules to guide the birds' movements and demonstrate, by means of simulations, that they tend to lead to stabilization into several of the well-known V-like formations that have been observed in nature. We also provide quantitative indicators that we believe are closely related to achieving V-like formations, and study their behavior over a large set of independent simulations.