For almost ten years chaos and fractals have been riding a wave that has enveloped many areas of mathematics and the natural sciences in its power, creativity and expanse Traveling far beyond the traditional bounds of mathematics and science to the distant shores of popular culture, this wave captures the attention and enthusiasm of a worldwide audience The fourteen chapters of the 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, Percolation and Strange Attractors Each Chapter is closed by a Program of the Chapter which provides computer code for a central experiment Two appendices complement the book, the first, by Yuval Fisher, discusses the details and ideas of fractal image compression The second, by Carl J.G Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals....
|Title||:||Chaos and Fractals: New Frontiers of Science|
|Publisher||:||Springer Berlin Auflage 2., corr Printing 1993|
|Number of Pages||:||193 Pages|
|File Size||:||593 KB|
|Status||:||Available For Download|
|Last checked||:||21 Minutes ago!|
Chaos and Fractals: New Frontiers of Science Reviews
This book is addressing readers who want to understand in more depth the theories around fractals and chaos. The classical introduction to into the subject is usually Mandelbrot's classic "The Fractal Geometry of Nature". However, I perceived the book as (now) outdated, not clearly organized and too high-level, thus nearly avoiding any deeper explanation in mathematical terms. Instead it is referring to a bunch of references. The essence of fractals is heard to grasp here.On the other hand, hard-core mathematical introductions exist (e.g. the very good though old book of K. J Falconer) which, however, don't help to grasp the essence and the beauty of the theories because of their limited focus and mathematical difficulties.Insofar, the book from Peitgen at al. is really a wonderful book addressing a large range of topics and explaining very well the mathematical concepts behind fractals and chaos. This is important because otherwise the whole subject reduces to watching nice pictures but not unfolding the deep common principles behind the different fractal structures.Really terrific are the first eight chapters introducing into the deterministic fractals. How the authors introduced fractals as the limit of symmetry transformations really opened up my mind.The book is also for people without too strong mathematical background since the (relatively) hardest mathematics are given in "side boxes" which can be overread the first time.This book is a must for everyone who wants to get a real understanding of fractals and chaos.
As good as this book is in depth, there are faults in the presentation that will put off the real beginner: like the use of set notation in the coverage of fractal compression. The basic code works and is translatable to most other languages. The documentaion of the code could be better. I get the feeling that the authors are writing in a foreign language and lack the common touch of a Clifford Pickover. Your unique Associates ID is: thefractaltransl.
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!
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.
I found the 1992 edition of this book at my local public library, and was (like all the other reviewers here) very impressed at the quality. The book deals with a highly technical subject, but does it in a way that you can follow even if you don't have advanced math training. The numerous color plates were also very beautiful. And to top it all off, there were "do it yourself" exercises at the end of the chapters, showing you how to program your computer to run these figures! OK, they use the old BASIC language, but still the code is clear enough that you can follow it and see what's really going on with these equations.So I was so pleased to see a copy of the updated edition at a bookstore. In particular, I was eager to see if they'd updated those "do it yourself" exercises for use with EXCEL. However, as I read through it I was disappointed to notice two changes from the previous edition: first, all of the programming examples had been eliminated; second, the print quality of the color plates was noticeably poorer. And I didn't see much new material added - in fact one of the reviews above observes that the text itself is virtually unchanged. Considering the steep price of this tome, these were significant points to consider. Used copies of the old edition cost under 20 bucks, and IMHO are a better deal (I ended up buying one). So if you're ready to buy, just do yourself (and your wallet) a favor and compare the two editions first.
I purchased this book when it first came out, during theinitial wave of popularity of fractals and chaos theory.Although the fadishness of chaos and fractals has dieddown, a number of solid applications for this theory haveappeared 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. Althoughcellular 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 ofclaiming 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 afantastic book. I recommend it for anyone in the appliedsciences (e.g., computer science, quantitative finance,geology, etc...). Even for the mathematically sophisticated itwill provide an valuable overview, which is difficult to obtainanywhere else.
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 like an "oldmsdos" folder and dig out the Qbasic files found there and fire them up. Even if you've never written a program, this kind of applied-use is a fine way to learn!For the right sort of reader, this is unquestionably a 5-star book.