CELLULAR AUTOMATA ͳ INNOVATIVE MODELLING FOR SCIENCE AND ENGINEERING Edited by Alejandro Salcido Cellular Automata - Innovative Modelling for Science and Engineering 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. 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ISBN 978-953-307-172-5 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 Quantum Computing 1 Information-Theoretic Modeling and Analysis of Stochastic Behaviors in Quantum-Dot Cellular Automata 3 Lei Wang, Faquir Jain and Fabrizio Lombardi Architectural Design of Quantum Cellular Automata to Implement Logical Computation 23 Alejandro León Magnetic QCA Design: Modeling, Simulation and Circuits 37 Mariagrazia Graziano, Marco Vacca and Maurizio Zamboni Conservative Reversible Elementary Cellular Automata and their Quantum Computations 57 Anas N. Al-Rabadi Quadra-Quantum Dots and Related Patterns of Quantum Dot Molecules: Basic Nanostructures for Quantum Dot Cellular Automata Application 95 Somsak Panyakeow Quantum Cellular Automata Controlled Self-Organizing Networks 113 Laszlo Gyongyosi and Sandor Imre Quantum-Chemical Design of Molecular Quantum-Dot Cellular Automata (QCA): A New Approach from Frontier Molecular Orbitals 153 Ken Tokunaga Contents Contents VI Materials Science 177 Modeling of Macrostructure Formation during the Solidification by using Frontal Cellular Automata 179 Dmytro S. Svyetlichnyy Point Automata Method for Dendritic Growth 197 Agnieszka Zuzanna Lorbiecka and Božidar Šarler Simulation of Dendritic Growth in Solidification of Al-Cu alloy by Applying the Modified Cellular Automaton Model with the Growth Calculation of Nucleus within a Cell 221 Hsiun-Chang Peng and Long-Sun Chao Mesoscopic Modelling of Metallic Interface Evolution Using Cellular Automata Model 231 Abdelhafed. Taleb and Jean Pierre Badiali Cryptography and Coding 263 Deeper Investigating Adequate Secret Key Specifications for a Variable Length Cryptographic Cellular Automata Based Model 265 Gina M. B. Oliveira, Luiz G. A. Martins and Leonardo S. Alt Cryptography in Quantum Cellular Automata 285 Mohammad Amin Amiri, Sattar Mirzakuchaki and Mojdeh Mahdavi Research on Multi-Dimensional Cellular Automation Pseudorandom Generator of LFSR Architecture 297 Yong Wang, Dawu Gu, Junrong Liu, Xiuxia Tian and Jing Li An Improved PRNG Based on the Hybrid between One- and Two- Dimensional Cellular Automata 313 Sang-Ho Shin and Kee-Young Yoo A Framework of Variant Logic Construction for Cellular Automata 325 Jeffrey Z.J. Zheng, Christian H.H. Zheng and Tosiyasu L. Kunii Robotics and Image Processing 353 Using Probabilistic Cellular Automaton for Adaptive Modules Selection in the Human State Problem 355 Martin Lukac, Michitaka Kameyama and Marek Perkowski Part 2 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part 3 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Part 4 Chapter 17 Contents VII Design of Self-Assembling, Self-Repairing 3D Irregular Cellular Automata 373 David Huw Jones, Richard McWilliam and Alan Purvis Cellular Automata for Medical Image Processing 395 Sartra Wongthanavasu Accelerating 3D Cellular Automata Computation with GP GPU in the Context of Integrative Biology 411 Jonathan Caux, Pridi Siregar and David Hill Chapter 18 Chapter 19 Chapter 20 Pref ac e Modelling and simulation are disciplines of major importance for science and engineer- ing. There is no science without models, and simulation has nowdays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The numerical solution of diff erential equations has for many years been a paradigm of the computational approaches for simulation. Nevertheless, some conceptually dif- ferent strategies for modelling and simulation of complex behaviour systems have been developed from the introduction of the innovative concept of cellular automata by Stanislaw Ulam and John Von Neumann in the early 1950s. Cellular automata are dynamical systems which consist of a fi nite-dimensional la ice, each site of which can have a fi nite number of states, and evolves in discrete time steps obeying a set of ho- mogeneous local rules which defi ne the system´s dynamics. These rules are defi ned in such a way that the relevant laws of the phenomena of interest are fulfi lled. Typically, only the nearest neighbours are involved in the updating of the la ice sites. The main a ractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, such as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has a racted the researchers’ a ention from a wide variety of divergent fi elds of the exact disciplines of science and engineering, but also of social sciences, and sometimes be- yond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very diff erent purposes. In this book, a number of innovative applications of cellular automata models in the fi elds of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented. Brief descriptions of these outstanding contribu- tions are provided in the next paragraphs. Quantum Computing. Chapter 1 presents an information-theoretic framework to in- vestigate the relationship between stochastic behaviors and achievable reliable per- formance in quantum cellular automata technology. The central idea is that quantum cellular automata devices can be modelled as a network of unreliable information processing channels. In Chapter 2, cellular automata with graphane structured mol- ecules and graphane nanoribbons to propagate and process digital information are proposed. The cells that make up the architecture of the automata correspond to the molecules and to sections of the nanoribbon. It is also intended to verify theoretically X Preface that the proposed system is scalable, and binary information can be stored, propa- gated and processed at room temperature. Chapter 3 describes a magnetic quantum dot cellular automata approach for twisting computation and its technological imple- mentation. The fundamental technological hypothesis (the snake-clock implementa- tion) is explained, and an example of circuit description is given, followed by a specifi c architectural solution adopted with the low-level details. The contribution presented in Chapter 4 extends and implements several of the reversible and quantum comput- ing concepts to the context of elementary cellular automata, and this includes a new method for modelling and processing via the reversibility property in the existence of noise. The main contribution is the creation of a new algorithm that can be used in noisy discrete systems modelling using conservative reversible elementary cellular automata and the corresponding quantum modelling of such discrete systems. This approach considers the important modelling and processing case which uses Swap- based operations to represent reversible elementary cellular automata even in the pres- ence of noise. Chapter 5 reviews self-assembly of InAs quantum dot molecules with diff erent features fabricated by the combination of conventional Stranski-Krastanow growth mode and modifi ed molecular beam epitaxy technique using thin or partial capping as well as droplet epitaxy. InGaAs quantum rings with square shaped nano- holes are realized by droplet epitaxy, which are utilized as nano-templates for quadra quantum dot molecules where four InAs quantum dots are situated at the four cor- ners of a square. This quadra quantum dot set is a basic quantum cellular automata cell for future quantum computation. Chapter 6 provides a brief overview of the basic properties of quantum information processing and analyzes the quantum versions of classical cellular automata models. Then it examines an application of quantum cel- lular automata, which uses quantum computing to realize real-life based truly random network organization. This abstract machine is called a quantum cellular machine, and it is designed for controlling a truly random biologically-inspired network, and to integrate quantum learning algorithms and quantum searching into a controlled, self-organizing system. Chapter 7 proposes a new and simple approach for designing high-performance molecular quantum cellular automata. It reviews two approaches for the theoretical study on the two-site molecular quantum cellular automata and dis- cusses the influence of complex charge n on the signal transmission through molecular quantum cellular automata. Materials Science. Chapter 8 of this section discusses a combined approach of a three- dimensional frontal cellular automata model with a fi nite element model which has been developed for modelling the macrostructure formation during the solidifi cation in the continuous casting line. This joint has allowed improving accuracy of model- ling. Calculated distribution of the temperature gives a basis for the simulation of macrostructure formation close to the real one. In Chapter 9, a novel point automata method is developed and applied to model the dendritic growth process. The main advantages of this method are: no need for mesh generation or polygonisation; the governing equations are solved with respect to the location of points (not polygons) on the computational domain; it allows rotating dendrites in any direction since it has a limited anisotropy of the node arrangements; it off ers a simple and powerful approach of cellular automata type simulations; it off ers straightforward node refi nement pos- sibility, and straightforward extension to 3D. Chapter 10 proposes a model based upon the coupling of a modifi ed cellular automaton model with the growth calculation of a nucleus in a given nucleation cell, to simulate the evolution of the dendritic structure in [...]... quantum-dot cellular automata, Journal of Vacuum Science and Technology, 1752-1755 Niemier, M., Alam, M., Hu, X S., Bernstein, G., Porod, W., Putney, M and DeAngelis, J (2007) Clocking structures and power analysis for nanomagnet-based logic devices, Proc of international symposium on Low power electronics and design , 26-31 22 Cellular Automata - Innovative Modelling for Science and Engineering Walus,... of Quantum Cellular Automata Isolation and characterization 20 Cellular Automata - Innovative Modelling for Science and Engineering of a covalently bonded square array of two ferrocenium and two ferrocene complexes, J Am Chem Soc., vol 125, 1522-1523 Momenzadeh, M., Huang, J and Lombardi, F (2005) Defect characterization and tolerance of QCA sequential devices and circuits, Defect and Fault Tolerance... lithographically made QCA devices Information-Theoretic Modeling and Analysis of Stochastic Behaviors in Quantum-Dot Cellular Automata (a) QCA Line 9 (b) QCA Inverter (c) QCA fanout (d) QCA Majority (e) QCA Crossbar Fig 4 Statistical channel models for different QCA devices 10 Cellular Automata - Innovative Modelling for Science and Engineering In addition to the above defects, device size and temperature will also... devices under cell displacement defects Information-Theoretic Modeling and Analysis of Stochastic Behaviors in Quantum-Dot Cellular Automata 17 (a) QCA Line (b) QCA Inverter (c) QCA Majority (d) QCA Crossbar (e) QCA Fanout Fig 8 Information transfer capacity of QCA devices under cell misalignment defects 18 Cellular Automata - Innovative Modelling for Science and Engineering QCA devices degrades quickly... , (2) 6 Cellular Automata - Innovative Modelling for Science and Engineering where H (Y | X ) is the conditional entropy of Y conditioned on X, and it is expressed as H (Y | X ) = − =− ∑ ∑ p( x, y) log2 ( p(y| x )) ∑ ∑ p( x ) p(y| x ) log2 ( p(y| x )), x ∈X y∈Y x ∈X y∈Y (3) where p( x, y) and p(y| x ) are the joint probability and conditional probability, respectively, of variables X and Y For a given... what engineers and scientists are doing about the application of the cellular automata techniques for modelling systems and processes in diverse disciplines, so as to produce innovative simulation tools and methods to support the development of science and engineering We also hope that the readers will find this book interesting and useful Lastly, we would like to thank all the authors for their excellent... technologies, the stochastic behaviors of QCA devices impose a significant 4 Cellular Automata - Innovative Modelling for Science and Engineering hurdle to reliable system integration for high performance and scalability These stochastic behaviors stem from the nondeterministic quantum mechanisms in combination with the large number of defects and variations from fabrication In particular, it is anticipated that... of a QCA device For QCA crossbars, only the width of horizontal lines is increased (as proposed in (Bhanja et al., 2006)) Some important phenomena are observed from the simulation results The information transfer capacity of 16 Cellular Automata - Innovative Modelling for Science and Engineering (a) QCA Line (b) QCA Inverter (c) QCA Majority (d) QCA Crossbar (e) QCA Fanout Fig 7 Information transfer... models for morphogenesis and existing techniques for designing self-assembling robotics Then, it introduces a cellular automata model for morphogenesis and determines the necessary conditions for its robust self-assembly and self-assembly to a pre-defined shape Finally, it demonstrates the model coordinating the self-assembly of 55,000 cell virtual robot Chapter 19 presents a number of cellular automata- based... Cellular Automata, Science, 1466-1468 Smith, C., Gardelis, S., Rushforth, A., Crook, R., Cooper, J., Ritchie, D., Lineld, E., Jin, Y and Pepper, M (2003) Realization of quantum-dot cellular automata using semiconductor quantum dots, Super lattices and Microstructures, vol 34, 195-203 Jiao, J., Long, G., Grandjean, F., Beatty, A and Fehlner, T (2003) Building blocks for the molecular expression of Quantum Cellular . CELLULAR AUTOMATA ͳ INNOVATIVE MODELLING FOR SCIENCE AND ENGINEERING Edited by Alejandro Salcido Cellular Automata - Innovative Modelling for Science and Engineering Edited by Alejandro. orders@intechweb.org Cellular Automata - Innovative Modelling for Science and Engineering, Edited by Alejandro Salcido p. cm. ISBN 978-953-307-172-5 free online editions of InTech Books and Journals. the cellular automata techniques for modelling systems and processes in di- verse disciplines, so as to produce innovative simulation tools and methods to support the development of science and