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!)

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.

This is truly a remarkable book. I thoroughly enjoyed just about everything in it. However, I had to buy TWO copies in order to read the entire book! The publisher made a printing error in my first copy in which the final 3 chapters of the book were omitted and replaced by a repeat of earlier chapters. The publisher refused to reply to my letter requesting a copy of at least the missing materials. However, the content is so interesting, that I bought another copy for a friend and read the final chapters before sending it off to the friend.

I bought this book because of its first chapter, in which the author presented a proof of the Pythagorean Theorem by Einstein. Of course, this is from a second or even third hand source. The author, Manfred Schroeder, heard this story from Schneider Lifson of the Weizmann Institute in Tel Aviv, who in turn has it from Eistein's assistant Ernst Strauss, to whom it was told by old Albert himself. However, Banesh Hoffmann told a different story in his article Some Einstein Anomalies, pp. 91-92, Albert Einstein: Historical and Cultural Perspectives. The Proof reconstructed by Hoffmann is similar to the one in Legendre's Elementary Geometry, but the one stated in this book uses areas exclusively.

I knew Hoffmann's story first and later the Schroeder's. So, I bought this book for a comparison. Were really TWO proofs given by Einstein? But, which one is more realistic? If I have to choose, the Hoffman reconstructed version seems to be more realistic as it is along the way of thinking during the turn of 20-th century. The story recorded in Schroeder's book is based on areas of similarity figures, which can be a little too far for someone who just started learning geometry. However, if the story was told by Einstein himself and if the story was passed down correctly and accurately, the proof is really a beautiful one. The question is: did Einstein tell two different stories to different persons? No one would get the correct answer know.

Easy to understand

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 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 .

Just love this book!!

Un recorrido agradable por una temática difícil de condensar en un sólo volumen. El autor logra un buen material sin exagerar en el uso de las matemáticas, pero tampoco ignorándolas. Buen libro. En cuanto a la compra: satisfecho en cuanto a calidad/precio y al tiempo de envío y embalaje.

Easy introduction to fractals. The author presents a lot of interesting facts without completely hiding the mathematical background. The storytelling is also good.

Para aqueles que buscam um livro que instrua sobre fractais, sua matemática e como construí-los ou identificá-los, saiba de antemão que este não é o livro que você está buscando. O texto deste trata-se de uma coletânea de vários artigos científicos e matemáticos, cujo objetivo é apresentar ao leitor o mundo dos fractais e a sua presença na dinâmica de sistemas, construções topológicas naturais, harmonia sonora,biologia e em sistemas cuja evolução obedece algum tipo de probabilidade.

Trata-se de um texto bastante informativo para aqueles que buscam saber sobre as várias características e aparições inusitadas dos fractais na natureza e como a foram identificados por pesquisadores do ramo. Porém, o leitor que busca algum tipo de teoria ou compreensão da matemática de fractais de forma generalizada irá encontrar-se extremamente frustrado.

Stickers on it hard to remove. Good book to start a more deeper journey through Chaos theory.

The explanation in this book could be better. The author certainly knows a lot, but he can never update this book to make it more whole. Not because it doesn't need to be but because the author died many years ago. I didn't think it was a good intro to fractals since many pieces of math simply cannot be applied more broadly as they are presented in this book. Overall, for the price it's not a bad book but there's better books out there on fractals, cellular automata and chaos.