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Gaussian self-affinity and fractals : globality, the Earth, 1/f noise, and R/S : selecta (old or new) volume H

Author: Benoit B Mandelbrot
Publisher: New York : Springer-Verlag, ©2002.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

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  Read more...

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Document Type: Book
All Authors / Contributors: Benoit B Mandelbrot
ISBN: 0387989935 9780387989938
OCLC Number: 123103320
Description: ix, 654 pages : illustrations ; 25 cm
Contents: Overview of fractals and multifractals (2000) --
I. Advances in Old but Open Topics (2000) --
1. Tile self-affinity: close-up on a versatile family (2000) --
2. Steps toward a definition of self-affine functions (2000) --
3. Fractal dimensions of Wiener Brownian motion, random walk, and their clusters: 2, 3/2, 4/3, 1, and the new "transient" 5/3 (2000) --
4. Still growing Weierstrass family of functions (M 1982F, 2000) --
5. Iso- and heterodiffusion, and statistics using the bridge range; mesodiffusion (2000) --
6. Diffusion self-affine fractal functions: their stationarity in logarithmic time (2000) --
II. Broad Continuing Issues (2000) --
7. Experimental power-laws suggest that self-affine scaling is ubiquitous in nature (2000) --
8. Recorded history and personal recollections (2000) --
III. Introductions from the 1960s --
9. Self-affinity and Hurst's law (M 1965h) --
10. Noah, Joseph and operational hydrology (M & Wallis 1968) --
IV. Fractional Brownian Motions --
11. Fractional Brownian motions, fractional noises and applications (M & Van Ness 1968) Appendix (2000) --
12. Computer experiments with fractional Gaussian noises. Part 1: Sample graphs, averages and variance (M & Wallis 1969a) --
13. Computer experiments with fractional Gaussian noises: Part 2: Rescaled bridge ranges and "pox diagrams" (M & Wallis 1969a) --
14. Computer experiments with fractional Gaussian noises. Part 3: Mathematical appendix (M & Wallis 1969a) --
15. Fast fractional Gaussian noise generator (M 1971f) --
16. Broken-line approximation to fractional noise (M 1972o) --
V. Fractional Brownian Surfaces --
17. Poisson approximation of the multi-temporal Brownian functions and generalizations (M 1975b) --
18. Geometrv of homogeneous scalar turbulence: iso-surface fractal dimensions 5/2 and 8/3 (M 1975f) --
19. Earth's relief, shape and fractal dimension of coastlines, and number-area rule for islands (M 1975w) --
20. Midpoint displacement cartoon surfaces (M 1988p) --
VI. Self-Affine Cartoons in Grids; Their Multiple Fractal Dimensions --
21. Self-affinity and fractal dimension (M 1985l) --
22. Diagonally self-affine fractal cartoons. Part 1: Mass, box and gap dimensions, local or global (M 1986t) --
23. Diagonally self-affine fractal cartoons. Part 2: Length and area "anomalies" (M 1986t) --
24. Diagonally self-affine fractal cartoons. Part 3: Anomalous Hausdorff dimension and multifractal "localization" (M 1986t) Foreword (2000) --
VII. R/S Analysis and Its Uses --
25. Robustness of R/S in measuring non-periodic global dependence (M & Wallis 1969c) --
26. Limit theorems on the self-normalized bridge range (M 1975z) --
27. Global dependence in geophysical and other records (M & Wallis 1969b) --
28. Secular pole motion and Chandler wobble (McCamy & M 1970) --
29. Clustering in a point process: intertoken histograms and R/S pox diagrams (Damerau & M 1973) --
30. Global (long-term) dependence in economics and finance (long foreword and excerpts from M 1969e, M 1971n, M 1972c) --
31. Fractal aspects of computer memories (foreword and the abstract of Voldman, M, Hoevel, Knight & Rosenfeld 1983).
Responsibility: Benoit B. Mandelbrot ; includes contributions by F.J. Damerau, M. Frame, K. McCamy, J.W. Van Ness, J.R. Wallis, and others.

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From the reviews of the first edition:"Written in Mandelbrot's unique, thought-provoking style, these papers and commentaries contain a wealth of ideas which will appeal to mathematicians, Read more...

 
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