Fractals: Form, Chance, and Dimension

作者：B. B. Mandelbrot, Michael Aizenman · 发表于：Physics Today · 年份：1979 · DOI：10.1063/1.2995555 · 被引用次数：2163 · 研究领域：Complex Systems and Time Series Analysis

This is the most extraordinarily beautiful book in thought and in form that I have read for many years, and that is all the more peculiar for its being a somewhat technically mathematical treatise. Fractals is a whole new field of mathematics that models the most interdisciplinary grab-bag of naturally occurring forms, such as coastlines and clouds, crystals, snowflakes and cosmological structures. This new English edition with its triking format and illustrations doe justice to the idio yncratic geniu of the author in a way that the parsimonious French ver ion did not. Mandelbrot, who ha had chairs in economics, engineering, physiology, as well as everal of the choice t plums of the world of mathematics, is a jack-of-all-mathematical trades to IBM. Both the term and the field of fractals are his invention and pet, though he is also reverently anecdotal about the' prior history of the concepts of wiggliness involved in Brownian motion and the work of Edmund Fournier D'Albe, Lewis Fry Richard on and the many cia ical mathematicians who hav contributed to this theory. The idea of fractals extend to both random and non-random sets, and is defined as a set for which the Hausdorff-Be icovitch dimension trictly exceeds the topologica] dimen ion. Both of the e dimensionalities lie between zero and the dimension of the Euclidean space in which one works. The topological dimension i always an integer for Brownian motion, for example, it is unity, whereas the Hausdorff-Besicovitch i of...