W H Freeman & Company
We have witnessed a revolution in the way we understand symmetry. In an astounding series of discoveries, and in an equally astounding number of cases, it was found that size changed while scale remained constant (scaling invariance). In other cases, scale changed, while size remained the same. Both phenomena have been identified as self-similarity.
Focusing on what the author describes as “perhaps the most pregnant of all of nature’s symmetries,” Fractals, Chaos, Power Laws reveals the extraordinary dimensions of the mathematical insights about the nature of physical reality. The general reader will get a comprehensive initiation into the startling consequences of self-similarity. The specialist will discover convergences in unexpected fields – as Manfred Schroeder explores the powerful applications of these symmetry concepts in physics, chemistry, music, and the visual arts. Everyone will marvel at the stunning computer-generated graphics that embody Schroeder’s insights.
From Leibniz’s infinitely long straight line, an early example of scaling invariance, and the rise of Cantor sets as a pristine example of self-similarity, the author traces the development of the concepts in mathematics and provides keen insights into the analytical power with which they describe a diverse range of seemingly different phenomena.
Told in a style that is at once illuminating and entertaining, the narrative encompasses in its broad sweep such areas as * deterministic chaos and strange attractors * iterated mappings * nonlinear dynamics * Cayley trees * cellular automata * random fractals * and related topics.
Manfred Schroeder served as a distinguished member of the research staff of AT&T Bell Laboratories for 33 years. From 1958 to 1969 he was Director of Acoustic and Speech Research at the labs. Since 1969, he has divided his time between Bell and the University of Goettingen, Germany, where he is Professor of Physics. Dr. Schroeder is also a founding member of the Institut de Recherche et Coordination Acoustique / Musique (IRCAM) of the Centre Pompidou in Paris.
Dr. Schroeder was one of the early practitioners of computer graphics for artistic purposes, winning first prize at the1969 International computer Art exhibition in Las Vegas. A holder of 45 U.S. patents for inventions in various fields, he won the Gold Medal of the Audio Engineering Society and the Lord Raleigh Medal in 1972 and 1987, respectively.
Schroeder is the author of the highly acclaimed Number Theory and Science and Communication (1984).