| 000 | 07087 a2200181 4500 | ||
|---|---|---|---|
| 020 | _a9780444528322 | ||
| 082 |
_a006.37 _bMIS |
||
| 100 | _aMishra, J. | ||
| 245 | _aL-System fractals | ||
| 260 |
_bElsevier _aAmsterdam _c2007 |
||
| 300 | _axiii,258,ip. | ||
| 440 |
_aMathematics in science and engineering Ed. by C. K. Chui _vVol.209 |
||
| 520 | _acontent Preface v Contents ix 1 Introduction to Fractals 1 1.1 Overview of fractals 2 1.2 Fractals vs. Computer Graphics 2 1.2.1 Chaotic Systems 3 1.2.2 Strange Attractor 5 1.2.3 Newton Raphson 7 1.3 Fractal Geometry 8 1.4 Categories of Fractals 12 1.4.1 Geometrical fractals 12 1.4.2 Algebraic fractals 13 1.4.3 Stochastic fractals 15 1.5 Fractals and Non-fractal Objects. 15 1.5.1 The sizes of the features of the fractal and non-fractal objects 16 1.5.2 The four measure properties of fractal. 17 1.6 Defining a fractal. 18 1.6.1 Definitions of related terms... 18 1.6.2 Definition of fractal 19 1.7 Applications for Fractals 19 1.8 Summary 21 2 Fractals and L-System 23 2.1 Reviews on L-system 23 2.2 Parallel grammars: A phenomenon 26 2.3 L-Systems 27 2.3.1 DOL-system 27 2.3.2 Fractals and graphic interpretation of strings 28 2.3.3 Bracketed L-systems and models of plants architecture.. 30 2.3.4 L-systems and Genetic Algorithms 31 2.4 Basic definitions of L-Systems 31 2.4.1 Fibonacci L-system 32 2.4.2 Types of L-systems 33 2.4.3 Thue-Morse L-system 35 2.4.4 Paper folding and the Dragon curve 36 2.5 Turtle graphics and L-systems 39 2.5.1 Branching and bracketed L-systems 41 2.5.2 Famous L-systems of mathematical history. 43 2.5.3 Self-similarity and scaling 45 2.6 Summary 47 3 Interactive Generation of Fractal Images 49 3.1 IPS and Fractals 49 3.2 Generation of Fractals 50 3.2.1 Multi Lens Copy Machine 51 3.3 Computer Implementation 55 3.3.1 The Random Algorithm 55 3.4 Designing Fractals 56 3.4.1 How does the program work 58 3.5 Software Package 60 3.5.1 Background 60 3.5.2 Computer Implementation 61 3.5.3 Sample Output 61 3.6 Mathematical Expression of IFS 67 3.6.1 RIFS 68 3.6.2 Modified MRCM 69 3.7 Summary 70 4 Generation of a Class of Hybrid Fractals 71 4.1 Background 71 4.1.1 Parallel grammar: A critical review 71 4.1.2 Rules for biological phenomenon 74 4.1.3 Some definitions and examples 76 4.1.4 Applications of L-System 78 4.1.5 Turtle graphics vs L-System 79 4.1.6 Generation of fractal figures 79 4.1.7 About L-System 81 4.1.8 An L-system example 81 4.1.9 Representing mathematical sequence in L-System 82 4.2 The Approach 84 4.2.1 Assumptions 84 4.2.2 Combination of L-Systems 86 4.2.3 The new L-System or the Hybrid L-System 87 4.2.4 The Algorithm 88 4.3 Experimentally Generated Fractals 89 4.3.1 Fractal figures for Fibonacci sequence and Koch curve 89 4.3.2 Fractal figures for Mathematical series 1 to n and Koch curve 90 4.3.3 Fractal figures based on different combinations 92 4.4 Variation on Koch Curves 93 4.5 Fractals with other Mathematical Sequences 95 4.6 Interpretation of Result 99 4.6.1 Comparison of Koch curve with Hybrid system 99 4.6.2 Arbitrary Figures 102 4.7 Summary 104 5 L-System Strings from Ramification Matrix 105 5.1 Definition of Terms 105 5.1.1 Modules 105 5.1.2 Productions 106 5.2 Parallel Rewriting Systems 106 5.3 An Elementary L-System Parser 107 5.3.1 The structure of an L-System module 107 5.3.2 L-System strings 107 5.3.3 Rewriting the L-System string 107 5.4 Generating The Tree 108 5.4.1 Parsing the L-System 108 5.5 Advantages and Disadvantages of L-Systems 109 5.6 Ramification Matrices 109 5.6.1 Compiling a matrix 109 5.6.2 Ramification matrix for basic branching scheme 109 5.6.3 Generation of L-system string from the ramification matrix 112 5.6.4 Normalisation of the matrix 113 5.7 Fractal Figures Using The Grammar 113 5.8 Summary 114 6 3D Modeling of Realistic Plants 117 6.1 Related Work 118 6.1. IDOL-systems 118 6.1.2 Edge Rewriting vs. Node Rewriting 119 6.1.3 Stochastic L-Systems 121 6.1.4 Context-sensitive L-system 121 6.1.5 Branching structures 122 6.1.6 Parametric L-Systems 122 6.2 Key Factors 123 6.2.1 Practicality 123 6.2.2 Realism 124 6.2.3 Rendering speed 124 6.3 Component Modeling 124 6.3.1 Practicality 125 6.3.2 Realism 126 6.3.3 Real-time Rendering 126 6.4 An Object-Oriented Approach To Modeling 127 6.4.1 Stem Component 129 6.4.2 Leaf Component 132 6.4.3 Tree Component 134 6.4.4 Radial Component 136 6.5 Other Tree Modeling 137 6.5.1 Tree Growth Visualisation 137 6.5.2 Adaptive L-system 140 6.5.3 DOL System with 3D Structure 140 6.5.4 Environment Interactive 142 6.6 Summary 148 7 Fractal Dimension 149 7.1 Self Similar Fractals 149 7.1.1 Fractals and Self-similarity 150 7.1.2 Length of the coast of Iceland 151 7.2 Extending To Fractal Surfaces 152 7.2.1 Mandelbrot's formula 152 7.2.2 Casey's Classification 153 7.2.3 Pentland's Method 154 7.3 Various Methods Of Fractal Dimension Calculation 155 7.3.1 Reticular cell counting method 155 7.3.2 Keller's Approach 156 7.3.3 Differential Box-Counting Method 157 7.4 Bound of the box size 158 7.4.1 Keller's Correction 158 7.4.2 Fractional Box-Counting Method 159 7.4.3 Mishra's Bounds 160 7.5 Multifractals 160 7.5.1 Multifractal Point Patterns 161 7.5.2 Multifractal Calculations on Generalized Sierpinski Triangles 162 7.6 Fractal dimension from the L-System 163 7.6.1 Fractal dimension of hybrid fractals from L-System 164 7.7 Summary 165 8 Research Directions of L-Systems 167 8.1 L-Systems on Data Base Management Systems 167 8.1.1 Retrieval, Indexing & storage 168 8.1.2 Queries 169 8.1.3 Text Summarization 170 8.1.4 Language, Semantics and Relevancy 170 8.1.5 Latent Semantics & Reduction Techniques 172 8.1.6 Datamining 172 8.2 Parsers, Compilers 174 8.3 Web Links 175 8.4 Tools 176 8.5 Recent field of Applications of L-Systems 177 8.5.1 Indexing and Data Mining in Multimedia Databases 178 8.5.2 L-Systems and Fractal Growth 178 8.5.3 Cellular Automata 178 8.5.4 Autonomous Agents 178 8.5.5 Explore Individual Differences in Handwriting 179 8.6 Classifiers, IPS and L-Systems 179 8.6.1 Iterated Function Systems (IFS 179 8.6.2 Lindenmeyer Systems (L-Systems 180 8.6.3 Schemas 180 8.6.4 Classifier Systems (CS 181 8.6.5 Reinforcement Learning (RL 181 8.6.6 LCS Learning Classifier Systems 182 8.6.7 Extended Classifier Systems 182 8.6.8 Finite State Machines (FSM 183 8.6.9 Constrained Generating Procedures (CGP 183 8.7 In the field of Animation 184 8.8 Some important research abstracts 194 8.9 Research Proposal on L-System 217 8.10 Summary 218 Bibliography 219 Appendix-A 227 Appendix-B 241 Appendix-C 245 Colour Section 247 Index 257 | ||
| 700 | _aMishra, S. N. | ||
| 890 | _aUSA | ||
| 891 | _aFA | ||
| 942 | _2ddc | ||
| 999 |
_c39264 _d39264 |
||