Customer Reviews

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

5 star:		(9)
4 star:		(2)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

What an excellent find! I'd been reading Per Bok's "How Nature Works" and realized I need a better grounding in the basics of fractal mathematics; this book turned out to be just the ticket.

Schroeder starst out with some simple, intuitive examples of curves and regions that do not scale to integral proportions, and from thse he develops and introduces the notion of the Hausdorf dimension of a curve. From there he introduces new concepts graphically- like Koch snowflakes and the Serpienski gasket- by first constructing them and then doing the analysis, introducing new concepts as needed to advance the illustration.

Often Schroeder starts with very non-geometric illustrations; his section on power laws begins with a discussion of language and word frequency, and from there he introduces Zipf's law, and then generalizes to characteristics of power law distributions in general- but not before treating the reading to a fascinating discourse on cognates and false cognates between languages- which he manages to weave into a discussion of self-similarity. Brilliant!

"Fractals, Chaos, Power Laws" could easily be used for a University-level introduction to fractal math, for graduate students or advanced undergrads- yet it's still readable enough to be a find introduction and entertainment to the reader with only a basic background in algebra and perhaps some calculus. The casual reader might not follow all the mathmatical arguments, but he or she could still glean much from this book. Highly recommended for the mathematically inclined looking for education or entertainment.

This book can be read in two different ways:

The first one is intended for the uninitiated who wants to get an introduction to chaos and fractals; the way Schroeder guides you into the chaotic phenomenae that occur everywhere around us is clear, elegant and funny. He plays with chaos and makes the reader part of this game.

The second way to read this book includes a warning for scholars: This is not a textbook! The mathematical background used to explain this game is strong. Shcroeder lets the committed reader to work with the maths by himself, so you must have paper, pencil, and computer near to you in order to enjoy the book's whole potential, in this case Shcroeder has all the experience and knowledge on the matter to guide you through "this infinte paradise" in a very firm way.

The only thing I'd wish from this book was a new hardcover edition, I've read it so many times that my copy is getting very spoiled.

If you are still interested after reading this book, but you want a little help with your maths then I'd recommend "Chaos Theory Tamed" by Garnett P. Williams. It will do the trick. However if you just want to fall in love with chaos without complications, then you should read "Chaos: The Making of a New Science" by James Gleick.

If you've had some background in this kind of mathematics, or are otherwise familiar with concepts like limits and Lebesgue measure, you should thoroughly enjoy this well-written and good-humored introduction to fractals, chaos, and related topics. Do not, however, undertake to read this book as an easy introduction to those topics, because Schroeder uses a number of terms without bothering to define them, and covers a lot of ground in each chapter, from the perspective of a non-mathematician/physicist, at least.

For a shorter, gentler introduction to this material, I recommend R.L. Devaney's "Chaos, Fractals, and Dynamics: Computer Experiments...," which contains BASIC code to allow you to play with these systems on your computer. If that piques your interest enough, you can then turn to Schroeder's book for a broader and fuller treatment of these ideas.

For the uninitiated! --The author combines insight with story telling. He has a story to tell, and does it well! Not only does he know the theory inside out, he has the ability to get accross the central points so it (almost) seems easy, in any case entertaining, using pictures (including cartoons), humor, and equations when they are needed. He further make clear the many fascinating links between chaos theory, algorithms, technology, and areas of pure math, such as number theory. Highly recommended!

This book is a complete guide of all possible situations in science where you may encounter chaos. It provides for every situation an intuitive as well as very formal view of every problem and the corresponding solution. The main drawback concerns its relative inaccessibility for non-scientific people, it requires a quite important scientific background to understand the formal part. Anyway, even for the lay-man, it can be interesting to read, in order to understand the widespread of chaos and non-linearity in real-life situations, not just the purely scientific-related ones.

However, the treatment is terrific, with excellent description and explanations of the how's and why's, at an intuitive level as well as a very rigorous one ! I don't think i've ever read a book of such a high quality...

This book is worth its price, and without a doubt deserves the time you'll need to go through it.

The best introductory book on fractals and chaos. It has a breath-taking wealth of topics, complete with the intuition behind them, the formulas, the drawings and pictures. A 'must read' for anyone who wants a serious introduction to these fascinating topics.

This book explores many cases of self similar structures that give rise to fractals .

It is not mathematically oriented and the few mathematical arguments are easy .

It is full of examples of anecdotical character demonstrating power laws and self similarity (concert halls , music , image treatment etc) .

There are also some nice pictures .

However it is not by any account a book concerning the chaos theory .

As a physicist I have been disappointed .

It is too long to be a book on fractal esthetics and it is too short and too anecdotical to be a book about non linear dynamics .

The only description I can find would be : entertaining mathematical games on the concept of iteration and self similarity .

This is a one of the best semi-technical mathematics books I ever read. What I mean by "semi-technical" is, you need somewhat of a math interest and education to appreciate it, and if you have that, you can read it casually. You don't need pen and paper; it's not a textbook. However, occasionally you will want to grab the pen and paper to verify what the author writes.

For an ex-math person as myself, this book is an eye-opener as to how many areas of life are touched by fractals and chaos theory. Everything from nature, to economic markets, to music, to just plain theoretical stuff is mentioned here. And the writer delivers it in a well-organized, lucid, entertaining, and passionate fashion. And it is well-illustrated, which really helped me understand....

I'm on my 3rd reading of this book since 1992, and if I wear out the book, I'm buying another one! I rank this up there with "Prime Obsession" as the two best non-textbook math books I ever read.

One of the best introductory books I've ever read about the subject. A good example of multidisciplinarity and a bridge between theoretical and practical studies. The author does not avoid mathematics, allowing accuracy and complete explanations, and does not exceed, making the book readable to beginners.

What a head-trip! While the Pearly Gates of Paradise may be more than a few minutes away, you are almost certain to enjoy the journey with this book in hand. I purchased this book from Amazon back in 2002 and apart from the curling cellophane-coated front cover, I have nothing but praise for it. It simply gets better, every single time I read it - not unlike sipping some fine vintage even as it ages.

It must be difficult to write a book on a subject so intrinsically mathematical while retaining a healthy, comprehensible tone with a twist of the ridiculous. Schroeder has an enviable sense of comic timing in addition to his peculiarly personalized insight into the world of Number Theory. It is pretty amazing, considering the broad and variable scope of his exposition that the entire opus did not descend into an inexorable chaotic mess of formulae. He skillfully manages to avoid the quagmire of complexity by properly abbreviating lengthy explanations with diagrams, pretty color prints and even the occasional cartoon aside. This leaves him enough time for the most engaging (not to mention informative) anecdotes which allows him to bring the reader into certain obscure fields of research - bilingual poetry, cheating at roulette and on how to kill Germans with Gift(s) - so to speak.

Do not be fooled by the casual tone of the book because this is anything but a cursory tour. In fact, if this is your first encounter with Chaos and Fractals, it may be better to have more than one supplementary text at hand. (I suggest Peitgen, Jurgens and Saupe's Chaos and Fractals: New Frontiers of Science.) Schroeder's book is written for serious students, who want to see some practical (and sometimes not-so-practical) applications of what were once mere mathematical monstrosities. Neither Weierstrass nor Cantor could have predicted that their little monsters would turn out to dominate the physical world. This book gives you an insightful look at how far non-differentiable functions have come since those early pioneering days.

Go ahead and buy this book. It is what every scientific book should aspire to be - brilliant and funny (exactly in that order!)