Contents -- Preface M. M. Novak -- Selected Topics in Mathematics, Physics, and Finance Originating in Fractal Geometry B. B. Mandelbrot -- 1 Introductory comments of various kinds -- 2 Complex Brownian bridge -- Brownian cluster and the dimension 4/3 of its boundary -- the self-avoiding plane Brownian motion -- 3 Explosive multiplication of new fractal constructions, dimensions (including negative ones), and Holder exponents -- 4 Tools of fractal analysis other than the dimensions: ramification and lacunarity -- 5 Fractality of the major fractal clusters in statistical physics -- 6 Interrelations between fractality and smooth variability: some cases may have a common origin in the usual partial differential equations -- 7 Iterates of the complex map z2 + c. Julia and Mandelbrot sets -- 8 Limit sets of Kleinian groups -- 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" -- 10 The variation of financial prices -- 11 The directly useful fractal -- 12 Fractals in the college and school classroom -- Acknowledgements -- References -- A Renewal Process of Mittag-Leffler Type F. Mainardi, R. Gorenflo and E. Scalas -- 1 Essentials of renewal theory -- 2 The Poisson process as a renewal process -- 3 A fractional generalization of the renewal Poisson process -- 4 The Mittag-Leffler distribution as limit for thinned renewal processes -- 5 Conclusions -- Acknowledgements -- References -- On the Activity of Absorbing Irregular Interfaces J. S. Andrade Jr., H. F. Da Silva, E. A. Henrique and B. Sapoval -- 1 Introduction -- 2 Laplacian Transport and the Theorem of Makarov -- 3 The Nonequilibrium Molecular Dynamics Model -- 4 The Random-Walk Model -- 5 Summary -- Acknowledgments -- References.

Fractal Deformation Using Displacement Vectors and Their Increasing Rates Based on Extended Unit Iterated Shuffle Transformation T. Fujimoto and N. Chiba -- 1 Introduction -- 2 Extended Unit Iterated Shuffle Transformation -- 3 Fractal Deformation by Applying IST to Displacement Vectors -- 4 Fractal Deformation by Applying IST to Increasing Rates of Displacement Vectors -- 5 Conclusion and Future Work -- References -- Multifractal and Stochastic Analysis of Electropolished Surfaces M. Haase, A. Mora and B. Lehle -- 1 Introduction -- 2 Characteristic length scales and scaling regions -- 3 Multifractal analysis based on wavelets -- 4 Stochastic Analysis -- 5 Conclusions -- References -- A Method for Numerical Estimation of Generalized Renyi Dimensions of Affine Recurrent IFS Invariant Measures T. Martyn -- 1 Introduction -- 2 Preliminaries -- 3 Lattice approximation of RIFS invariant measure -- 4 Computing Renyi dimensions -- 5 Discussion of results -- Acknowledgments -- References -- Nonlinear Dynamics and Prediction of the Caspian Sea Level N. G. Makarenko, L. M. Karimova, Y. B. Kuandykov and M. M. Novak -- 1 Introduction -- 2 Caspian Sea Level Data Description and Methods of Analysis -- 3 CSL Forecasting by Artificial Neural Networks -- 4 Conclusions -- 5 Acknowledgments -- References -- Self-similarity in Plants: Integrating Mathematical and Biological Perspectives P. Prusinkiewicz -- 1 Introduction -- 2 Identity-in-parallel and iterated function systems -- 3 L-systems, recurrence systems, and self-similarity -- 4 Catenative formulas -- 5 Data-flow network representation of recurrence systems -- 6 Extension to branching structures -- 7 Relation between topological and geometric self-similarity -- 8 Conclusions -- Acknowledgments -- References.

Cognitive Scale-free Networks as a Model for Intermittency in Human Natural Language P. Allegrini, P. Grigolini and L. Palatella -- 1 Introduction -- 2 DE and concepts -- 3 Scale-free networks, intermittency and the Zipf's law -- 4 Conclusions -- References -- The Complexity of Biological Ageing D. Stauffer -- 1 Introduction -- 2 Demography -- 3 Why do we age? -- 4 Simulations of mutation accumulation -- 5 Sex -- 6 Conclusion -- Acknowledgements -- References -- Fitting Curves by Fractal Interpolation: An Application to the Quantification of Cognitive Brain Processes M. A. Navascues and M. V. Sebastian -- 1 Introduction -- 2 Fractal Interpolation of a Continuous Function in a Compact Real Interval -- 3 Fit of sampled data by fractal interpolation -- 4 Application to the quantification of cognitive brain processes -- Acknowledgments -- References -- Stochastic and Regular Components in Forcing of Solar Large-scale Structures E. Tikhomolov -- 1 Introduction -- 2 Model -- 3 Results -- 4 Discussion -- References -- Fast, Efficient On-line Simulation of Self-similar Processes O.D.Jones -- 1 Introduction -- 2 EBP processes -- 3 Simulation algorithm -- 4 Proofs -- References -- Fractal Geometry in the Arts: An Overview Across The Different Cultures N.Sala -- 1 Introduction -- 2 Fractal components in the arts -- 3 Conclusions -- 4 References -- Fractal Properties and Characterization of Road Profiles P. Legrand, J. Levy Vehel and M.-T. Do -- 1 Introduction and background -- 2 The road profiles -- 3 Fractal analysis -- 4 Results -- References -- Fractal Distributions of Temperature, Salinity and Fluorescence in Spring 2001-2002 in South San Francisco Bay K. Fisher and W. Kimmerer -- 1 Introduction -- 2 Data and Methods -- 3 Results -- 4 Discussion -- 5 Conclusions -- 6 Acknowledgements -- References.

Characterization of Fractal Structures Through a Hausdorf Measure Based Method F.Nekka and J.Li -- 1 Introduction -- 2 Hausdorff Measure Spectrum Functions of Uniform Cantor Sets. -- 3 Applications -- 4 Conclusion -- Acknowledgments -- References -- Fractal Scattering Indicators for Urban Sound Diffusion P. W. Woloszyn -- 1 Introduction: Problem and purpose -- 2 Diffusion through oblique incident wave -- 3 Diffraction and structure factor of a multiscalc rough boundary surface -- 4 Application : a Facade scattering characterization -- 5 Experimental validation: In situ measurements -- 6 Conclusion -- 7 References -- Binomial Multiplicative Model of Critical Fragmentation H. Katsuragi, D. Sugino and H. Honjo -- 1 Introduction -- 2 Experiment -- 3 Model -- 4 Discussion -- 5 Conclusions -- Acknowledgments -- References -- Study on the Improved Fractal Interpolation Surface of the Attitude and Surface of Fault H. Sun and H. Xie -- 1. Introduction -- 2. The principles of fractal interpolation surface on a rectangle field -- 3. Attitude analyses of the fault surface -- 4. Improved fractal interpolation surface of the fault surface -- 5. Fractal interpolation of the fault surface -- 6. Conclusions -- Acknowledgements -- References -- A Deterministic Power Domain Algorithm for Fractal Image Decompression N. Nikolaou, A. Kakos and V. Drakopoulos -- 1 Introduction -- 2 A Computational Model -- 3 The Plotkin Power Domain Algorithm -- 4 The Algorithm and its Complexity -- 5 Conclusions -- Appendix -- References -- Comparative Dynamical Scaling Analysis of Quasi-2D Electrodeposited Silver Patterns under Localized and Non-localized Random Quenched Noise M. A. Pasquale, S. L. Marchiano and A. J. Arvia -- 1 Introduction -- 2 Experimental -- 3 Results and Discussion -- A cknowledgment s -- References.

Epidermal Ridges: Positional Information Coded in an Orientational Field M. B. Nguyen, V. Fleury and J.-F. Gouyet -- 1 Introduction -- 2 Epidermal Ridges -- 3 The model -- 4 Results -- 5 Conclusion -- References -- Multiscale Principal Components A. Saucier -- 1 Introduction -- 2 Overview of our approach to the construction of multiscale principal components -- 3 Construction of the first order MFC -- 4 Construction of higher order MFCs -- 5 Diadic MPCs -- 6 Conclusions -- References -- Coexistence of Doublon and Dendrite Structure with Phase-Field Model S. Tokunaga and H. Sakaguchi -- 1. Introduction -- 2. Model equation -- 3. Result and discussion -- 4. Summary -- References -- Fractality and Fractal Dimension in Mesoamerican Pyramid Analysis G. Burkle-Elizondo, A. G. Fuentes-Larios and R. D. Valdez-Cepeda -- References -- Morphological Variety in Crystal Growth of Mercury (II) Chloride on Agar Slides /. A. Betancourt-Mar and E. J. Sudrez-Dominguez -- References -- 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 -- References -- Fractals and Plant Water Use Efficiency A. Bari, G. Ayad, A. Martin, J. L. Gonzalez-Andujar, M. Naclrit, and I. Elouafi -- References -- Need and Feasibility of Applying L-system Models in Agricultural Crop Modeling L. Pachepsky, M. Kaul, Ch. Walthall, C. Daughtry and]. Lydon -- Fractal Detection and Avoidance Using RS Statistics and Honeybee Navigational Skills in Dynamic Environments R.L.Walker -- References -- Signal and Image Processing with FracLab J. Levy Vehel and P. Legrand -- References -- Author Index.