Discrete Iterated Function Systems

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Written for researchers and developers applying Integrated Function Systems in the creation of fractal images, this book presents a modification of a widely used probabilistic algorithm for generating IFS-encoded images. The book also includes a discussion of how IFS techniques can be applied to produce animated motion pictures.

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Editorial Reviews

Fractals can be used for encoding a large class of digitized color images in computer graphics. The author takes the original encoding method a step further. He analyzes a modified version of the widely used probabilistic algorithm generating IFS-encoding images, explores the connections and disparities of continuous and discrete IFSs, and illustrates some surprising implications of his discretization method. He also discusses how IFS techniques can be applied to produce animated motion pictures. Contains eight color plates and many b&w illustrations. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781568810157
  • Publisher: Taylor & Francis
  • Publication date: 5/15/1993
  • Pages: 200

Table of Contents

List of Figures
1 Introduction 1
2 Deterministic Theory of Iterated Function Systems 9
2.1 Preliminaries 10
2.2 Contractive and Affine Transformations 12
2.3 Iterated Function Systems 16
2.4 Iterated Function Systems with Condensation 28
2.5 Self-Covering and Encoding 31
3 Probabilistic Theory of Iterated Function Systems 39
3.1 Generation Algorithm 41
3.2 Stochastic Model 44
3.3 Self-Covering Property 48
3.4 Invariance Condition and Encoding 49
3.5 Mixing Algorithm 52
3.6 Another Look at the Stochastic Model 54
3.7 Other Applications of the Invariance Condition 58
4 The Round-Off Process 69
4.1 Definition of the Round-Off Process 70
4.2 Properties of the Round-Off Version of a Single Contractive Transformation on R[superscript 2] 75
4.3 Examples of Round-Off Versions of Contractive Transformations on R[superscript 2] 88
4.4 Limiting Properties of the Round-Off Process 124
5 Animation 147
5.1 Continuity Considerations 149
5.2 A Discontinuity Example 151
5.3 Making Movies 154
5.4 Graphics Equipment 167
Bibliography 171
Index 175
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