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L-System Fractals, Volume 209 [Kõva köide]

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(Indira Gandhi Institute of Technology, Department of Computer Science and Application, Sarang, Talcher, Orissa, India.), (College of Engineering and Technology, Department of Information Technology, Bhubaneswar, India.)
  • Formaat: Hardback, 274 pages, kõrgus x laius: 229x152 mm, kaal: 570 g, Illustrated; Illustrations, unspecified
  • Sari: Mathematics in Science & Engineering
  • Ilmumisaeg: 08-Jan-2007
  • Kirjastus: Elsevier Science Ltd
  • ISBN-10: 0444528326
  • ISBN-13: 9780444528322
Teised raamatud teemal:
L-System Fractals, Volume 209Suurem pilt
  • Formaat: Hardback, 274 pages, kõrgus x laius: 229x152 mm, kaal: 570 g, Illustrated; Illustrations, unspecified
  • Sari: Mathematics in Science & Engineering
  • Ilmumisaeg: 08-Jan-2007
  • Kirjastus: Elsevier Science Ltd
  • ISBN-10: 0444528326
  • ISBN-13: 9780444528322
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780444528322.html
Märksõnad:
The book covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals.



Key Features:
- Fractals generated from L-System including hybrid fractals
- Dimension calculation for L-system fractals
- Images & codes for L-system fractals
- Research directions in the area of L-system fractals
- Usage of various freely downloadable tools in this area



- Fractals generated from L-System including hybrid fractals
- Dimension calculation for L-system fractals
- Images & codes for L-system fractals
- Research directions in the area of L-system fractals
- Usage of various freely downloadable tools in this area

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 IFS and Fractals
49
3.2 Generation of Fractals
50
3.2.1 Multi Lens Copy Machines
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
6.1.1 DOL-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, IFS 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