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

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 papers and presents a number of striking new observations and conjectures. The mathematical tools so discussed will be valuable to diverse scientific communities.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 Brownian functions, best known as the mathematical tools behind the celebrated fractal landscapes. Extensive introductory material preceding the reprints incorporates striking new observations and conjectures. This book explores the fractal themes of ?self-affinity? and ?globality.? The ubiquity of ?wild? temporal and spatial variability led Mandelbrot, in the early 1960?s, to conclude that those phenomena lie beyond the usual statistical techniques and represent a new state of indeterminism. New mathematical tools are needed, and this book contributes to their development.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

From the reviews of the first edition:

Written in Mandelbrots 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 Socil/