Thinking in Patterns: Fractals and Related Phenomena in Nature

Contents......Page 8
Preface M. M. Novak......Page 12
1 Introductory comments of various kinds......Page 14
2 Complex Brownian bridge; Brownian cluster and the dimension 4/3 of its boundary; the self-avoiding plane Brownian motion......Page 20
3 Explosive multiplication of new fractal constructions, dimensions (including negative ones), and Holder exponents......Page 23
4 Tools of fractal analysis other than the dimensions: ramification and lacunarity......Page 26
5 Fractality of the major fractal clusters in statistical physics......Page 30
6 Interrelations between fractality and smooth variability: some cases may have a common origin in the usual partial differential equations......Page 32
7 Iterates of the complex map z2 + c. Julia and Mandelbrot sets......Page 36
8 Limit sets of Kleinian groups......Page 38
9 The study of power law probability distributions and the notion that variability and randomness can fall into distinct \"states,\" ranging from \"mild\" to \"slow\" and \"wild\"......Page 41
10 The variation of financial prices......Page 42
11 The directly useful fractal......Page 44
Acknowledgements......Page 45
References......Page 46
1 Essentials of renewal theory......Page 48
2 The Poisson process as a renewal process......Page 51
3 A fractional generalization of the renewal Poisson process......Page 52
4 The Mittag-Leffler distribution as limit for thinned renewal processes......Page 55
5 Conclusions......Page 56
Acknowledgements......Page 57
References......Page 59
1 Introduction......Page 60
2 Laplacian Transport and the Theorem of Makarov......Page 61
3 The Nonequilibrium Molecular Dynamics Model......Page 64
4 The Random-Walk Model......Page 67
References......Page 68
1 Introduction......Page 70
3 Fractal Deformation by Applying IST to Displacement Vectors......Page 71
4 Fractal Deformation by Applying IST to Increasing Rates of Displacement Vectors......Page 74
References......Page 81
1 Introduction......Page 82
2 Characteristic length scales and scaling regions......Page 84
3 Multifractal analysis based on wavelets......Page 85
4 Stochastic Analysis......Page 87
5 Conclusions......Page 90
References......Page 91
1 Introduction......Page 92
2 Preliminaries......Page 93
3 Lattice approximation of RIFS invariant measure......Page 96
4 Computing Renyi dimensions......Page 99
5 Discussion of results......Page 101
References......Page 103
1 Introduction......Page 104
2 Caspian Sea Level Data Description and Methods of Analysis......Page 105
3 CSL Forecasting by Artificial Neural Networks......Page 110
4 Conclusions......Page 113
References......Page 114
1 Introduction......Page 116
2 Identity-in-parallel and iterated function systems......Page 117
3 L-systems, recurrence systems, and self-similarity......Page 118
4 Catenative formulas......Page 122
5 Data-flow network representation of recurrence systems......Page 123
6 Extension to branching structures......Page 124
7 Relation between topological and geometric self-similarity......Page 125
8 Conclusions......Page 129
References......Page 130
1 Introduction......Page 132
2 DE and concepts......Page 134
3 Scale-free networks, intermittency and the Zipf\'s law......Page 139
4 Conclusions......Page 141
References......Page 142
2 Demography......Page 144
3 Why do we age?......Page 148
4 Simulations of mutation accumulation......Page 149
5 Sex......Page 152
References......Page 153
1 Introduction......Page 156
2 Fractal Interpolation of a Continuous Function in a Compact Real Interval......Page 157
3 Fit of sampled data by fractal interpolation......Page 160
4 Application to the quantification of cognitive brain processes......Page 161
References......Page 166
1 Introduction......Page 168
2 Model......Page 169
3 Results......Page 172
4 Discussion......Page 176
References......Page 177
2 EBP processes......Page 178
3 Simulation algorithm......Page 182
4 Proofs......Page 186
References......Page 189
1 Introduction......Page 190
2 Fractal components in the arts......Page 191
3 Conclusions......Page 200
4 References......Page 201
2 The road profiles......Page 202
3 Fractal analysis......Page 204
4 Results......Page 206
References......Page 211
1 Introduction......Page 212
2 Data and Methods......Page 213
3 Results......Page 217
4 Discussion......Page 220
5 Conclusions......Page 222
References......Page 223
1 Introduction......Page 226
3 Applications......Page 227
References......Page 233
2 Diffusion through oblique incident wave......Page 234
3 Diffraction and structure factor of a multiscalc rough boundary surface......Page 236
4 Application : a Facade scattering characterization......Page 240
5 Experimental validation: In situ measurements......Page 242
6 Conclusion......Page 244
7 References......Page 245
1 Introduction......Page 246
2 Experiment......Page 247
3 Model......Page 250
4 Discussion......Page 252
Acknowledgments......Page 254
References......Page 255
1. Introduction......Page 256
2. The principles of fractal interpolation surface on a rectangle field......Page 257
3. Attitude analyses of the fault surface......Page 260
4. Improved fractal interpolation surface of the fault surface......Page 263
6. Conclusions......Page 266
References......Page 267
1 Introduction......Page 268
2 A Computational Model......Page 269
3 The Plotkin Power Domain Algorithm......Page 270
4 The Algorithm and its Complexity......Page 274
5 Conclusions......Page 275
Appendix......Page 277
References......Page 278
1 Introduction......Page 280
2 Experimental......Page 281
3 Results and Discussion......Page 282
References......Page 289
1 Introduction......Page 292
2 Epidermal Ridges......Page 294
3 The model......Page 298
4 Results......Page 300
5 Conclusion......Page 302
References......Page 303
1 Introduction......Page 304
3 Construction of the first order MFC......Page 305
4 Construction of higher order MFCs......Page 306
5 Diadic MPCs......Page 308
6 Conclusions......Page 312
References......Page 313
1. Introduction......Page 314
2. Model equation......Page 315
3. Result and discussion......Page 317
4. Summary......Page 318
References......Page 321
Fractality and Fractal Dimension in Mesoamerican Pyramid Analysis G. Burkle-Elizondo, A. G. Fuentes-Larios and R. D. Valdez-Cepeda......Page 322
References......Page 323
Morphological Variety in Crystal Growth of Mercury (II) Chloride on Agar Slides /. A. Betancourt-Mar and E. J. Sudrez-Dominguez......Page 324
References......Page 325
Fractal Characteristics of Bainbridge Crater Lake Sediment Gray-scale Intensity Data Documenting the Frequency and Intensity of Holocene El Nino/Southern Oscillation Events N. A. Bryksina and W. M. Last......Page 326
References......Page 327
Fractals and Plant Water Use Efficiency A. Bari, G. Ayad, A. Martin, J. L. Gonzalez-Andujar, M. Naclrit, and I. Elouafi......Page 328
References......Page 329
Need and Feasibility of Applying L-system Models in Agricultural Crop Modeling L. Pachepsky, M. Kaul, Ch. Walthall, C. Daughtry and]. Lydon......Page 330
Fractal Detection and Avoidance Using RS Statistics and Honeybee Navigational Skills in Dynamic Environments R.L.Walker......Page 332
References......Page 333
Signal and Image Processing with FracLab J. Levy Vehel and P. Legrand......Page 334
References......Page 335
Author Index......Page 336