|
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 new 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 Leibnitz'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 the 1969 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 Rayleigh Medal in 1972 and 1987, respectively.
Schroeder is the author of the highly acclaimed Number
Theory in Science and Communication (1984).
|
