Fractals’ Physical Origin and Properties

Abstract

CONTENTS Part 1. Multifractals and Turbulence A Class of Multinomial Multifractal Measures with Negative (Latent) Values for the "Dimension" f(a) .•.... B.B. Mandelbrot . . 3 Some Aspects of the Fractal Approach to the Fully Developed Turbulence . . . . . . . . . . . . . . . • . . . . . . . . . . . 31 A. Vulpiani Nonlinear Variability in Geophysics: and Analysis . . D. Schertzer and S. Lovejoy Multifractal Simulations .... 49 Part 2. Fractal Properties of Critical Fluctuations and Polymers Fractal Critical Phenomena in Two Dimensions and Gonformal Invariance B. Duplantier ...... 83 Fractal Structure of Ising and Potts Clusters: Static and Dynamic Approach . • . • . A. Coniglio 123 Part 3. Fractal Growth Models: General Features Diffusion-Limited Aggregation: Recent Developments P. Meakin and S. Tolman New Theoretical Methods for Fractal Growth L. Pietronero, A. Erzan and C. Evertsz . . . . 137 169 Continuum Description of the Active Zones • . . . • . . . . . . . . • 193 z. Racz Multifractality, Scaling, and Diffusive Growth . . . . . . . . . . . 205 T.C. Halsey Is There a Phase Transition in the Multifractal Spectrum of DLA? . . 217 J. Lee, P. Alstrom and H.E. Stanley vii Part 4. Application of Fractal Growth Models to Physical Phenomena Fractals and Patterns in Electrodeposition L.M. Sander and D.G. Grier 229 On the Passihle Application of Fractal Scaling Ideas in Dendritic Growth . . . . R.C. Ball . . . . . . . 239 Realistic Models of Dielectric Breakdown . . . . • . • . • . . . • . • 243 H.J. Wiesmann Cluster-Cluster Aggregation with Dipole-Dipole Interactions R. Botet, G. Helgesen, A.T. Skjeltorp, P.M. Mors and R. Jullien 259 Shapes of Deterministic Cracks Obtained Under Shear . . . . • . • . . 269 H.J. Herrmann Part 5. Diffusion and Vibrations on Fractals Superlocalization, Anomalaus Diffusion and Self Avoiding Walks on Fractals . . . . . . . . . . . . . . . . . A. Aharony and A.B. Harris 279 Observations of Fractons . . . E. Courtens, R. Vacher and J. Pelous . . . . . . . . . . . . . . . 285 Part 6. Diffusion Fronts and Invasion Pereclation Diffusion, Intercalation and Invasion Noise B. Sapoval, M. Rosso, J.F. Gouyet and Y. Boughaleb Dynamics of Invasion and Dispersion Fronts . . . . . J. Feder, T. J~ssang, L. Furuberg, K.J. Mäl~y, F. Boger and A. Aharony 297 307 Part 7. Random Surfaces Fractal Behavior of Tethered Networks . M. Kardar \ Surface Growth, Directed Polymers, and 1/f Noise . . . . . . . . . . Y.C. Zhang 327 337 Part 8. Large Scale Distribution of Matter in the Universe The Fractal Nature of the Galaxy Distribution . . P.H. Coleman Index . 349 36