Fractal Growth Phenomena (2nd Edition) / Edition 2

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Editorial Reviews

As much as anything, fractals are the study of what might have been. This much needed resource for the study of the complexity of patterns offers insights for both researchers and interested readers alike. No previous background in fractals is assumed, however, an understanding of higher mathematics such as linear algebra and differential equations is useful. Includes a color plate of fractals developed in the book. Software is available. Paper edition (unseen), $38. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9789810206680
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 6/28/1992
  • Edition description: Second Edition
  • Edition number: 2
  • Pages: 488

Table of Contents

Preface to the First Edition
1 Introduction 1
Pt. I Fractals
2 Fractal Geometry
2.1 Fractals as mathematical and physical objects 9
2.2 Definitions 13
2.3 Types of fractals 19
3 Fractal Measures
3.1 Multifractality 48
3.2 Relations among the exponents 52
3.3 Fractal measures constructed by recursion 56
3.4 Geometrical multifractality 65
4 Methods for Determining Fractal Dimensions
4.1 Measuring fractal dimensions in experiments 74
4.2 Evaluation of numerical data 81
4.3 Renormalization group 89
References 97
Pt. II Cluster Growth Models
5 Local Growth Models
5.1 Spreading percolation 105
5.2 Invasion percolation 111
5.3 Kinetic gelation 114
5.4 Random walks 119
6 Diffusion-limited Growth
6.1 Diffusion-limited aggregation (DLA) 137
6.2 Diffusion-limited deposition 167
6.3 Dielectric breakdown model 174
6.4 Other non-local particle-cluster growth models 178
7 Growing Self-affine Surfaces
7.1 Eden model 186
7.2 Ballistic aggregation 194
7.3 Ballistic deposition 197
7.4 Theoretical results 203
8 Cluster-cluster Aggregation (CCA)
8.1 Structure 215
8.2 Dynamic scaling for the cluster size distribution 226
8.3 Experiments 249
References 261
III Fractal Pattern Formation
9 Computer Simulations
9.1 Equations 272
9.2 Models related to diffusion-limited aggregation 278
9.3 Generalizations of the dielectric breakdown model 288
9.4 Boundary integral methods 294
10 Experiments on Laplacian Growth
10.1 Viscous fingering 302
10.2 Crystallization 318
10.3 Electrochemical deposition 326
10.4 Other related experiments 330
References 336
IV Recent Developments
11 Cluster Models of Self-similar Growth
11.1 Diffusion-limited aggregation 344
11.2 Fracture 364
11.3 Other models 375
11.4 Theoretical approaches 380
12 Dynamics of Self-affine Surfaces
12.1 Dynamic scaling 387
12.2 Aggregation models 390
12.3 Continuum equation approach 396
12.4 Phase transition 401
12.5 Rare events dominated kinetic roughening 405
12.6 Multiaffinity 413
13 Experiments
13.1 Self-similar growth 422
13.2 Self-affine growth 438
References 454
App. A. Algorithm for generating diffusion-limited aggregates 465
App. B. Construction of a simple Hele-Shaw cell 469
App. C. Basic concepts underlying multifractal measures 471
Author Index 475
Subject Index 483
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