Gaussian Self-Affinity and Fractals - Globality, The Earth, 1/f Noise, and R/S

Benoit Mandelbrot is a world-renowned scientist whose pioneering research significantly advanced the field of fractal geometry. This is the third volume of his Selected Works, focusing on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented. Extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools discussed will be valuable to diverse scientific communities.

List of contents

Advances in Old But Open Topics.- Broad Continuing Issues.- Introductions from the 1960s.- Fractional Brownian Motions.- Fractional Brownian Surfaces.- Self-Affine Cartoons in Grids; Their Multiple Fractal Dimensions.- R/S Analysis and Its Uses.

About the author

Benoit B. Mandelbrot, geb. 1924 in Warschau, arbeitete als Mathematiker lange Zeit bei IBM, ist Honorarprofessor an der Yale University und Erfinder der fraktalen Geometrie. Mandelbrot lebt in Scarsdale, New York.

Summary

Benoit Mandelbrot is a world-renowned scientist whose pioneering research significantly advanced the field of fractal geometry. This is the third volume of his Selected Works, focusing on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented. Extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools discussed will be valuable to diverse scientific communities.

Additional text

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, statisticians, scientists and economists alike. It is a book both for dipping into and for detailed study, making readily accessible seminal papers which contain ideas that are as relevant now as when first published." (K. Falconer, Proceedings of the Edinburgh Mathematical Society, Vol. 48, 2005)

"This book contains the author’s works in areas ranging from statistics, mathematics, physics, hydrology to economics and finance … as well as more than 200 pages of new material written especially for this volume. … To summarize, Volume H of Mandelbrot’s Selecta is a major contribution to the understanding of wild self-affine variability and randomness. I believe that … it will have a great impact on future research in mathematics, statistics, physics and other applied areas." (Yimin Xiao, Zentralblatt MATH, Vol. 1007, 2003)

"This book is a complete and encyclopaedic synthesis of problems and themes in self-affinity, fractals, multifractal geometry and globality. … a very exhaustive and complete bibliography on the different connected subjects (with more than 500 references) may be very useful for researchers or users." (Michèle Mastrangelo-Dehen, Mathematical Reviews, Issue 2003 a)

"This volume is volume H of a program of publications of selected works (old and new) of Benoit B. Mandelbrot. … The most valuable feature of the book is to bring together highly important papers … for this reason this book should be in the library of any scientist interested in the origin of the concepts of self-affinity and fractals and their numerous applications in science." (Christian Michaux, Simon Stevin Bulletin, 2003)

Report

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, statisticians, scientists and economists alike. It is a book both for dipping into and for detailed study, making readily accessible seminal papers which contain ideas that are as relevant now as when first published." (K. Falconer, Proceedings of the Edinburgh Mathematical Society, Vol. 48, 2005)
"This book contains the author's works in areas ranging from statistics, mathematics, physics, hydrology to economics and finance ... as well as more than 200 pages of new material written especially for this volume. ... To summarize, Volume H of Mandelbrot's Selecta is a major contribution to the understanding of wild self-affine variability and randomness. I believe that ... it will have a great impact on future research in mathematics, statistics, physics and other applied areas." (Yimin Xiao, Zentralblatt MATH, Vol. 1007, 2003)
"This book is a complete and encyclopaedic synthesis of problems and themes in self-affinity, fractals, multifractal geometry and globality. ... a very exhaustive and complete bibliography on the different connected subjects (with more than 500 references) may be very useful for researchers or users." (Michèle Mastrangelo-Dehen, Mathematical Reviews, Issue 2003 a)
"This volume is volume H of a program of publications of selected works (old and new) of Benoit B. Mandelbrot. ... The most valuable feature of the book is to bring together highly important papers ... for this reason this book should be in the library of any scientist interested in the origin of the concepts of self-affinity and fractals and their numerous applications in science." (Christian Michaux, Simon Stevin Bulletin, 2003)

Product details

• Authors: Benoit Mandelbrot, Benoit B. Mandelbrot, Benoît B. Mandelbrot
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 03.01.2002
• EAN: 9780387989938
• ISBN: 978-0-387-98993-8
• No. of pages: 654
• Dimensions: 158 mm x 240 mm x 43 mm
• Weight: 1086 g
• Illustrations: X, 654 p.
• Series: Selecta; Selecta
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; B, geometry, Mathematics and Statistics, Applications of Mathematics, Engineering mathematics, Applied mathematics