Chaos and Fractals: New Frontiers of Science

by Dietmar Saupe, Hartmut Jürgens, Heinz-Otto Peitgen

Book Overview

The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot set, Julia sets, cellular automata, L-systems,... This description may be from another edition of this product.

• Format: Hardcover
• Language: English
• ISBN: 0387979034
• ISBN13: 9780387979038
• Release Date: January 1992
• Publisher: Springer
• Length: 984 Pages
• Weight: 5.20 lbs.
• Dimensions: 2.3" x 7.9" x 9.5"

Customer Reviews

Chaos & Fractals

Awesome book. You can devour so much with the content.

Simply a fantastic book

I purchased this book when it first came out, during the initial wave of popularity of fractals and chaos theory. Although the fadishness of chaos and fractals has died down, a number of solid applications for this theory have appeared in areas like computer graphics, finance, modeling computer network traffic and data compression.I have purchased a number of books on fractals and chaos andhow these concepts can be applied in a number of areas. Ihave yet to see a better introduction to the topic. This isa core reference and I keep coming back to it again and again.In the spectrum of popular science books, this is definitelyon the technical end. You do not need an advanced backgroundin mathematics as you do for some books on chaos and fractals,but the authors do not shy away from equations. However, theideas are clearly presented. I have used this book as areference for developing software for fractal brownian motionand Hurst exponent estimation."Chaos and Fractals" covers a great deal of material. On a fewoccasions I found that the algorithms or explaination weredifficult to follow. In some cases, like the generation ofGaussian random numbers, I found better, simpler algorithms. When this book was written, fractals and chaos were fairly new.It is difficult to avoid comparing this book to an even thickerbook, "A New Kind of Science" by Stephen Wolfram. Although cellular automata, the core topic of "A New Kind of Science"are not exactly new, Wolfram claims new and profoundperspectives. Many, including this reviewer, feel that Wolfram'sclaims are overblown and egotistical (he has a bad habbit of claiming credit for innovation, even as he cites other work).The authors of "Chaos and Fractals" do not make exaltedclaims for this work. Yet without any fanfare, this bookreally does deliver profound ideas. This is simply a fantastic book. I recommend it for anyone in the applied sciences (e.g., computer science, quantitative finance, geology, etc...). Even for the mathematically sophisticated itwill provide an valuable overview, which is difficult to obtainanywhere else.

Excellent for intermediate knowledge of chaos

This book is a great entertainer for anyone who wants to spend many evenings "playing with chaos". The code in the book is a little dated (BASIC), but you won't have problems to use it as a good reference. The book will guide you through the understanding of the exciting realm of chaos and its hidden monsters. Chaos and fractals are subjects that sound modern, interesting and eye-catching in the most of the cases. However, the applications and implications of chaos in the real world constitute the great achievement of human knowledge that the concept represents.The lecture of this book doesn't require an extensive knowledge of math (but it would be helpful), it requires many will and passion for rediscovering your conception of the universe instead. Before reading this book I'd recommend "Chaos: the Making of a New Science" by James Gleick and for those who are looking for a more compact but challenging material "Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise" by Manfred Schroeder will be just fine.

Add some DEPTH to your "Recreational Mathematics"

I spent quite a bit of time looking for a good "fractals" book. For me, this is it. It is not a book for everyone, though. I'll try to offer guidelines to help you decide if it is for you. In summary: (a) its not just a picture book, but extremely visual, (b) its not math-intense but asks for math-comfort and offers options and (c) its not only for computer jockeys, but offers repeated links to that approach.This book is doubtless great for a high-school or college course in fractals. But I think it is also a worthy buy, albeit a pricey one, for a certain type of layperson with a fascination for mathematics presented in some depth. If you enjoy math but find some of the "popularizations" a bit too shallow, then the realm of fractals and chaos is a great place to explore in depth. This is a fine guidebook for that exploration."Chaos and Fractals" is not a book for the reader who is primarily fascinated with the visual representations of fractals. BUT it i!s chock-full of b/w illustrations (686 by the authors count) and nicely sprinkled with gorgeous color plates. The visual element is not central, but is very strongly represented and I found that almost every important concept was enhanced by the addition of a diagram or illustration.This is definitely a book that delves into the mathematics of fractals. It does so in a well-crafted dual-track form. The core of the book should be comfortable and enjoyable mathematical reading for anyone with a sound and fairly current familiarity with high school math (Not that such "currency" suggests its only for youngsters! This old-timer preserves essentially that level of math by regular exposure to recreational math and the like). On the second track, the book provides mathematically in-depth views of selected topics. This is really nice if you like to stretch your mathematical horizons since you can use the core to steady your foundation understanding of a topic and then dive int!o the advanced mathematical topics at will; mustering strategic retreat when necessary, without loss of face, but sometimes learning how more advanced mathematics can be used.Finally, the book makes an effort to scaffold some computer exploration of fractal concepts that succeeded for me but might not for you. For every chapter the authors provide a "Program of the Chapter" which allows exploration of one or more of the fractal forms and concepts explored therein. These are usually quite short and are written in Microsoft BASIC. This latter might be a problem for some. Nowadays, users with more advanced operating systems might not know where to find their version of BASIC (and it might not even be supplied), much less how to fire it up. I would not belabor the BASIC program element too much except that experimenting with such code is an excellent way for anyone to better understand an algorithmic process. A program is, after all, such a process - a sequence of !discrete steps. I'd urge you to search your Windows disk for something

Complex, but excellent

While Chaos and Fractals isn't really a book for the layman, I highly recommend it for those of you out there who want a deep and comprehensive look at these things. I've read several fractal books, some simple (FractalVision: Making Fractals Work For You), some highly mathematical (Fractal Image Compression, Science of Fractals), but this is easily the best of the lot, not only for in-depth but understandable reading, but also for separation. If you only want to learn about bifurcation in repeated iteration, or only about strange attractors, just pick the appropriate chapter. If you don't want to know about the more complex proofs, skip them; they're in small print and set off with lines to mark them as optional. I do recommend some mathematical education and an interest in (not necessarily a talent for) proofs to get the most from this book. They cite a lot of stuff that you probably haven't seen before if you haven't had some college calculus, at least the basics. And you won't understand the more complex stuff (basic topology, mainly) unless you've had some kind of proofs-based calc course. However, even without that, it's a _really_ neat book. There's a lot here that even the layman can understand, it's just that he'll be intimidated by the set-off parts that prove the results he's only skimming. I highly recommend this to anyone who is serious about fractals, or thinks they might try to be so in the future. It will take quite some time for even a dedicated fractal enthusiast to become bored with the book, even if it's the only one you own.

This is the best book every written about Chaos and fractals

This is the absolute best book on chaos and fractals, it is not extremely complex so someone with little math or science background can understand it yet it goes into massive details and provides all formulas and equations with explanations, the entire book is easy to understand and contains so much knowledge. If you buy one book to deal with chaos and fractals it should be this one, it is the best!