CELLULAR AUTOMATA ͳ SIMPLICITY BEHIND COMPLEXITY Edited by Alejandro Salcido Cellular Automata - Simplicity Behind Complexity Edited by Alejandro Salcido Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Iva Lipovic Technical Editor Teodora Smiljanic Cover Designer Martina Sirotic Image Copyright Shebeko, 2010. Used under license from Shutterstock.com First published March, 2011 Printed in India A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Cellular Automata - Simplicity Behind Complexity, Edited by Alejandro Salcido p. cm. ISBN 978-953-307-230-2 free online editions of InTech Books and Journals can be found at www.intechopen.com Part 1 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Preface IX Land Use and Population Dynamics 1 An Interactive Method to Dynamically Create Transition Rules in a Land-use Cellular Automata Model 3 Hasbani, J G., N. Wijesekara and D.J. Marceau Cellular-Automata-Based Simulation of the Settlement Development in Vienna 23 Reinhard Koenig and Daniela Mueller Spatial Dynamic Modelling of Deforestation in the Amazon 47 Arimatéa C. Ximenes, Cláudia M. Almeida, Silvana Amaral, Maria Isabel S. Escada and Ana Paula D. Aguiar Spatial Optimization and Resource Allocation in a Cellular Automata Framework 67 Epaminondas Sidiropoulos and Dimitrios Fotakis CA City: Simulating Urban Growth through the Application of Cellular Automata 87 Alison Heppenstall, Linda See, Khalid Al-Ahmadi and Bokhwan Kim Studies on Population Dynamics Using Cellular Automata 105 Rosana Motta Jafelice and Patrícia Nunes da Silva CA in Urban Systems and Ecology: From Individual Behaviour to Transport Equations and Population Dynamics 131 José Luis Puliafito Contents Contents VI Dynamics of Traffic and Network Systems 157 Equilibrium Properties of the Cellular Automata Models for Traffic Flow in a Single Lane 159 Alejandro Salcido Cellular Automata for Traffic Modelling and Simulations in a Situation of Evacuation from Disaster Areas 193 Kohei Arai, Tri Harsono and Achmad Basuki Cellular Automata for Bus Dynamics 219 Ding-wei Huang and Wei-neng Huang Application of Cellular Automaton Model to Advanced Information Feedback in Intelligent Transportation Systems 237 Chuanfei Dong and Binghong Wang Network Systems Modelled by Complex Cellular Automata Paradigm 259 Pawel Topa Cellular Automata Modeling of Biomolecular Networks 275 Danail Bonchev Simulation of Qualitative Peculiarities of Capillary System Regulation with Cellular Automata Models 301 G. Knyshov, Ie. Nastenko, V. Maksymenko and O. Kravchuk Dynamics of Social and Economic Systems 321 Social Simulation Based on Cellular Automata: Modeling Language Shifts 323 Francesc S. Beltran, Salvador Herrando, Violant Estreder, Doris Ferreres, Marc-Antoni Adell and Marcos Ruiz-Soler Cellular Automata Modelling of the Diffusion of Innovations 337 Gergely Kocsis and Ferenc Kun Cellular Automata based Artificial Financial Market 359 Jingyuan Ding Some Results on Evolving Cellular Automata Applied to the Production Scheduling Problem 377 Tadeusz Witkowski, Arkadiusz Antczak, Paweł Antczak and Soliman Elzway Part 2 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Part 3 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Contents VII Statistical Physics and Complexity 399 Nonequilibrium Phase Transition of Elementary Cellular Automata with a Single Conserved Quantity 401 Shinji Takesue Cellular Automata – a Tool for Disorder, Noise and Dissipation Investigations 419 W. Leoński and A. Kowalewska-Kudłaszyk Cellular Automata Simulation of Two-Layer Ising and Potts Models 439 Mehrdad Ghaemi Propositional Proof Complexity and Cellular Automata 457 Stefano Cavagnetto Biophysical Modeling using Cellular Automata 485 Bernhard Pfeifer Visual Spike Processing based on Cellular Automaton 529 M. Rivas-Pérez, A. Linares-Barranco and G. Jiménez, A. Civit Design and Implementation of CAOS: An Implicitly Parallel Language for the High-Performance Simulation of Cellular Automata 545 Clemens Grelck and Frank Penczek Part 4 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Pref ac e In the early 1950s, at the suggestion of Stanislaw Ulam, John Von Neumann introduced the cellular automata as simple mathematical models to investigate self-organisation and self-reproduction. Cellular automata make up a very important class of completely discrete dynamical systems. The physical environment of cellular automata is consti- tuted of a fi nite-dimensional la ice, with each site having a fi nite number of discrete states. The evolution in time of a cellular automaton goes on in discrete steps, and its dynamics is specifi ed by some local transition rule, fi xed and defi nite. In spite of their conceptual simplicity, which allows for an easiness of implementation for computer simulation, and a detailed and complete mathematical analysis in principle, the cel- lular automata systems are able to exhibit a wide variety of amazingly complex be- havior. This feature of simplicity behind complexity of cellular automata has a racted the researchers’ a ention from a wide range of divergent fi elds of study of science, which extends from the exact disciplines of mathematical physics up to the social ones, and beyond. In fact, nowadays, cellular automata are a core subject in the sciences of complexity. Thus, numerous complex systems containing many discrete elements with local interactions, and their complex collective behaviour which emerge from the interaction of a multitude of simple individuals, have been and are being conveniently modelled as cellular automata. For example, the dynamical Ising model, gas and fl uid dynamics, traffi c fl ow, various biological issues, growth of crystals, nonlinear chemical systems, land use and population phenomena and many others. Moreover, cellular automata are not the only models in natural sciences such as biology, chemistry and physics, but they are also, thanks to their complete space-time and state discreteness, appropriate models of parallel computation. Thus, cellular automata permit descrip- tions of natural processes in computational terms (computational biology, computa- tional physics), but also of computation in biological and physical terms (artifi cial life, physics of computation). In this book the versatility of cellular automata for modelling a wide diversity of com- plex systems is underlined through the study of a number of outstanding problems with the cellular automata innovative techniques. This book comprises twenty fi ve contributions organized in four main sections: Land Use and Populations Dynamics; Dy- namics of Traffi c and Network Systems; Dynamics of Social and Economic Systems; and Statis- tical Physics and Complexity. Brief descriptions of the book chapters are presented in the following paragraphs. Land Use and Populations Dynamics. Chapter 1 describes a semi-automated, inter- active method that was designed and implemented to dynamically create transition X Preface rules and calibrate a land-use CA model. The proposed method combines the benefi ts of conditional and mathematical rules and is adaptable in terms of number of land- use classes, and spatial and temporal scale of the input data. Chapter 2 presents and describes a cellular automata model for simulating the population distribution of the city of Vienna from 1888 to 2001. It has also developed a sensible and robust concept for the explanation of the driving forces of urban development processes, and it was shown that the development of the population density can be essentially regulated by infrastructure investments. In Chapter 3, the deforestation processes in a region called São Félix do Xingu, located in east-central Amazon, are simulated with a cellular automata model called Dinamica EGO. It consists of an environment that embodies neighbourhood-based transition algorithms and spatial feedback approaches in a sto- chastic multi-step simulation framework. The modelling experiment demonstrated the suitability of the adopted model to simulate processes of forest conversion, unravelling the relationships between site a ributes and deforestation in the area under analysis. Chapter 4 demonstrates that the heuristic search methods for the solution of spatial optimization problems have to be designed in accordance with the spatial character of the fi eld under study, which can be fi  ingly modelled by means of cellular automata. Two basic approaches are presented in this chapter to pursue a balance between local and global characteristics. Chapter 5 demonstrates the potential of cellular automata as a tool for urban planning and development using two models and case studies, one from Saudi Arabia and the other from the Republic of Korea. The strengths and weak- nesses of the models are discussed, including areas for further development. Chapter 6 presents three cellular automata that simulate the behavior of the population dynamics of three biological systems. The first one deals with artificially-living fish divided into two groups: sharks (predators) and fish that are part of their food chain (preys). The second model introduces a simulation of the HIV evolution in the blood stream of posi- tive individuals with no antiretroviral therapy. The last model extends the previous one and considers the HIV dynamics in individuals subject to medical treatment and the monitoring of the medication potency and treatment adhesion. Finally, Chapter 7 explores some of the fundaments of cellular automata models and the reasons why these are being so widely applied nowadays, particularly to urban systems and ecol- ogy, all of which seem to be connected directly to the fact that the transport equations are common as much to the socioeconomic phenomena as to physics. Dynamics of Traffi c and Network Systems. Chapter 8 presents an overview of the ba- sic cellular automata models for traffi c fl ow. A maximum entropy approach for analyz- ing the equilibrium properties of the cellular automata models for multi-speed traffi c fl ow in a single lane highway is also proposed and discussed. It is shown, in particular, that the traffi c cellular automata models of Nagel-Schreckenberg and Fukui-Ishibashi evolve rapidly towards steady states very close to equilibrium. In Chapter 9, a modifi ed model of the car-following Nagel-Schreckenberg model is proposed by incorporating the agent and diligent driver into it. The modifi ed evaluation of the proposed param- eter, the fundamental diagram, spatio-temporal pa erns, eff ect of lane-changing and car-following with respect to the evacuation time, combination parameter of diligent and agent driver in the case of evacuation time and the eff ectiveness are investigated. Chapter 10 presents a simple cellular automaton model to study the typical bus dynam- ics in a modern city. At a first stage, the nontrivial fluctuations are prescribed by the stochastic moving of bus interacted with the stochastic arrival of passengers, and at a second stage, the bus schedule interrupted by the traffi c lights is examined. The city [...]... Gohnai, Y., & Watanabe, K., 2007 Cellular automata modeling of fire spread in built-up areas: A tool to aid community-based planning for disaster mitigation Computers, Environment and Urban Systems 31(4): 441-460 22 Cellular Automata - Simplicity Behind Complexity Pan, Y., Roth, A., Yu, Z., & Doluschitz, R., 2010 The impact of variation in scale on the behavior of a cellular automata used for land-use change... broad meaning cellular automata now has Chapter 13 shows that cellular automata modelling technique could partially fill the gap in describing the dynamics of biomolecular networks While not able to provide exact quantitative results, it is shown that the cellular automata models capture essential dynamic patterns, which can be used to control the dynamics of networks and pathways Cellular automata models... in a Land-use Cellular Automata Model 5 Fig 1 Location of the study area; the dashed line represents the western limit of the study area Fig 2 Historical land-use trends in the study area The historical land-use maps also indicate that a considerable amount of land-use transition occurred in the study area during the period considered (Table 1) 6 Cellular Automata - Simplicity Behind Complexity From... of cellular automata The field of propositional proof complexity was born in the 1970s from two fields connected with computers: automated theorem proving and computational complexity theory Here it is shown how propositional logic and techniques from propositional proof complexity can give a new proof of Richardson’s Theorem, a famous theorem in this field Also, some complexity results regarding cellular. .. incorporates the effects of adaptability into the traffic cellular automata Simulations demonstrate that adopting these optimal information feedback strategies provide a high efficiency in controlling spatial distribution of traffic patterns Chapter 12 presents the application of the cellular automata paradigm for modelling network systems The combination of cellular automata and graph structure was successfully applied... overview of cellular automata modelling approaches to socio-economic systems with emphasis on the spreading of innovations The philosophy of bottom-up approaches of agent based models is outlined, and the typical set of cellular automata rules which have been proven successful during the past years in the field are described As a specific example, there is a detailed presentation of cellular automata for... Dragicevic, S., 2006 Assessing cellular automata model behaviour using a sensitivity analysis approach Computers, Environment and Urban Systems 30: 921-953 Lau, K H., & Kam, B H., 2005 A cellular automata model for urban land-use simulation Environment and Planning B 32: 247-263 Li, X., & Yeh, A G.-O., 2000 Modelling sustainable urban development by the integration of constrained cellular automata and GIS International... principal components analysis and cellular automata for spatial decision making and urban simulation Science in China, 45(6): 521-529 Li, X., & Yeh, A G.-O., 2002b Neural-network-based cellular automata for simulating multiple land use changes using GIS International Journal of Geographical Information Science 16(4): 323-343 Li, X., & Yeh, A G.-O., 2004 Data mining of cellular automata s transition rules... domain wall theory is applied to the elementary cellular automata Diffusive behavior of the domain wall is discussed as well Chapter 20 intends to show how simple cellular automata definitions allow construction of models reflecting physical properties of real systems, and to present how a complicated system evolution can be investigated with the help of cellular automata In particular, the model of many two-level... factors for the calibration of a land-use cellular automata model using Rough Set theory Computers, Environment and Urban Systems, in press White, R., Engelen, G., & Uljee, I., 1997 The use of constrained cellular automata for highresolution modelling of urban land-use dynamics Environment and Planning B 25: 323-343 Wu, F., 2002 Calibration of stochastic cellular automata, the application to rural-urban . CELLULAR AUTOMATA ͳ SIMPLICITY BEHIND COMPLEXITY Edited by Alejandro Salcido Cellular Automata - Simplicity Behind Complexity Edited by Alejandro Salcido Published. Kowalewska-Kudłaszyk Cellular Automata Simulation of Two-Layer Ising and Potts Models 439 Mehrdad Ghaemi Propositional Proof Complexity and Cellular Automata 457 Stefano Cavagnetto Biophysical Modeling using Cellular. Ruiz-Soler Cellular Automata Modelling of the Diffusion of Innovations 337 Gergely Kocsis and Ferenc Kun Cellular Automata based Artificial Financial Market 359 Jingyuan Ding Some Results on Evolving Cellular