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Gaussian Self-Affinity and Fractals Book

Gaussian Self-Affinity and Fractals
Gaussian Self-Affinity and Fractals, This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of self-affinity and globality are presented, while extensive introductory material, written especially for this book, precedes the p, Gaussian Self-Affinity and Fractals has a rating of 4.5 stars
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Gaussian Self-Affinity and Fractals, This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of self-affinity and globality are presented, while extensive introductory material, written especially for this book, precedes the p, Gaussian Self-Affinity and Fractals
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  • Gaussian Self-Affinity and Fractals
  • Written by author Benoit Mandelbrot
  • Published by Springer-Verlag New York, LLC, September 2007
  • This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented, while extensive introductory material, written especially for this book, precedes the p
  • Benoit Mandelbrot¿s pioneering research in fractal geometry has affected many areas of mathematics, physics, finance and other disciplines. The papers reprinted in this third volume of his Selected Works center on a detailed study of fractional Brown
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Authors

Preface (2000)1
Overview of fractals and multifractals (2000)9
IAdvances in Old but Open Topics (2000)49
1Tile self-affinity: close-up on a versatile family (2000)50
2Steps toward a definition of self-affine functions (2000)83
3Fractal dimensions of Wiener Brownian motion, random walk, and their clusters: 2, 3/2, 4/3, 1, and the new "transient" 5/3 (2000)111
4Still growing Weierstrass family of functions (M 1982F, 2000)142
5Iso- and heterodiffusion, and statistics using the bridge range; mesodiffusion (2000)155
6Diffusion self-affine fractal functions: their stationarity in logarithmic time (2000)172
IIBroad Continuing Issues (2000)187
7Experimental power-laws suggest that self-affine scaling is ubiquitous in nature (2000)187
8Recorded history and personal recollections (2000)204
IIIIntroductions from the 1960s231
9Self-affinity and Hurst's law (M 1965h)231
10Noah, Joseph and operational hydrology (M & Wallis 1968)236
IVFractional Brownian Motions253
11Fractional Brownian motions, fractional noises and applications (M & Van Ness 1968) Appendix (2000)254
12Computer experiments with fractional Gaussian noises. Part 1: Sample graphs, averages and variance (M & Wallis 1969a)283
13Computer experiments with fractional Gaussian noises: Part 2: Rescaled bridge ranges and "pox diagrams" (M & Wallis 1969a)306
14Computer experiments with fractional Gaussian noises. Part 3: Mathematical appendix (M & Wallis 1969a)327
15Fast fractional Gaussian noise generator (M 1971f)339
16Broken-line approximation to fractional noise (M 1972o)357
VFractional Brownian Surfaces361
17Poisson approximation of the multi-temporal Brownian functions and generalizations (M 1975b)363
18Geometrv of homogeneous scalar turbulence: iso-surface fractal dimensions 5/2 and 8/3 (M 1975f)368
19Earth's relief, shape and fractal dimension of coastlines, and number-area rule for islands (M 1975w)390
20Midpoint displacement cartoon surfaces (M 1988p)402
VISelf-Affine Cartoons in Grids; Their Multiple Fractal Dimensions423
21Self-affinity and fractal dimension (M 1985l)425
22Diagonally self-affine fractal cartoons. Part 1: Mass, box and gap dimensions, local or global (M 1986t)437
23Diagonally self-affine fractal cartoons. Part 2: Length and area "anomalies" (M 1986t)453
24Diagonally self-affine fractal cartoons. Part 3: Anomalous Hausdorff dimension and multifractal "localization" (M 1986t) Foreword (2000)463
VIIR/S Analysis and Its Uses481
25Robustness of R/S in measuring non-periodic global dependence (M & Wallis 1969c)483
26Limit theorems on the self-normalized bridge range (M 1975z)517
27Global dependence in geophysical and other records (M & Wallis 1969b)538
28Secular pole motion and Chandler wobble (McCamy & M 1970)562
29Clustering in a point process: intertoken histograms and R/S pox diagrams (Damerau & M 1973)584
30Global (long-term) dependence in economics and finance (long foreword and excerpts from M 1969e, M 1971n, M 1972c)601
31Fractal aspects of computer memories (foreword and the abstract of Voldman, M, Hoevel, Knight & Rosenfeld 1983)611
Comulative Bibliography613
Index637


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