Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise

by Manfred Schroeder

Self-similarity is a profound concept that shapes many of the laws governing nature and underlying human thought. It is a property of widespread scientific importance and is at the centre of much of the recent work in chaos, fractals, and other areas of current research and popular interest. Self-similarity is related to svmmetry and is an attribute of many physical laws: particle physics and those governing Newton's laws 0 , gravitation. Symmetry, found throughout the biological universe, is also a basic property of the mathematical universe. In this book the author explores the ideas of scaling, self-similarity, chaos and fractals as they appear throughout the universe of pure and applied mathematics. Because of his formidable research experience, stretching from the acoustical modelling of concert halls to pure number theory, Schroeder is able to take the reader on an intellectual excursion through this vast forest of topics.

Genres: Mathematics, Science, Reference, Physics, Nonfiction, Biology

429 pages, Hardcover

First published July 15, 1992

Reviews

[Paige McLoughlin · Rating 5 out of 5]

A classic book on chaos and fractals that I have consulted many times over the years. One of my favorites. College-level mathematics is probably needed to handle most of the material but it is fascinating. It seems nature's book is written with a lot of fractals and self-similar objects at varying scales, also tends to follow power laws for scaling. You will learn about fractal dimensions, and coastline of England, Hausdorf and box-counting metrics, Various kinds of statistical noise, and the power spectrums of White, Brown, Pink, and Black noise, percolation of forest fires, Logistic curves, period doubling, Feigenbaum constants, Koch curves, and cantor dust. This book has the works and some equations so keep that college math handy.

[Yates Buckley · Rating 4 out of 5]

Lovely math book that reviews across many fragments how certain phenomena, and mathematical questions relate to chaos, fractals and power laws.

What is frustrating is that inevitably you will find yoir favourites and be annoyed that the author only dedicated 3 pages to the problem you really care about.

A little too diverse and fragmented... but a fun math book.

[Thomas Ray]

QC174.17 S9 S38 1991 AMP Library

[Andrew · Rating 5 out of 5]

.Required reading for the professional and layman alike
.A readable treatment of frequently ignored examples in appl math

[Nathen]

I couldn't understand the math but the rest of it was really informative, and I got transitivity from this book.