Product Description

Fractals are unique patterns left behind by the unpredictable movements -- the chaos -- of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap -- all of these are fractals. Learn to recognize them and you will never again see things in quite the same way.

Fractals permeate our lives, appearing in places as tiny as the surface of a virus and as majestic as the Grand Canyon. From ancient tribal peoples to modern painters to the animators of Star Wars, artists have been captivated by fractals and have utilized them in their work. Computer buffs are wild about fractals as well, for they can be generated on ordinary home computers.

In Fractals: The Patterns of Chaos, science writer John Briggs uses over 170 illustrations to clearly explain the significance -- and more importantly, the beauty -- of fractals. He describes how fractals were discovered, how they are formed, and the unique properties different fractals share. Fractals is a breathtaking guided tour of a brand new aesthetic of art, science, and nature. It will revolutionize the way you see the world and your place within it.

* Contains a special bibliography listing fractal generating software for desktop computers ... Read more

Customer Reviews (13)

The best introductory guide to fractals and chaos
Though this book is now out of print it has not yet been surpassed (or even replaced) as an inhtroduction to the worelds of fractal illustarations. The photographs are astouding - and this leads the reader to read the print to find out more about the patterns that this book describes. Though the book is about mathematical ideas there is adearth of complicated mathematical formulae. It is easy reading for anyone who can add, subtract and multiply (no division!) andwho understand the very simplest algebra. I have used this book in a course I teach at our local Senior College and all the students love it.I am anxiously awaiting a second updated edition.

staggeringly beautiful
Technically this book is good.The images, however, are staggeringly beautiful.I think Dr. Briggs teaches esthetics, which is the study of beauty.Of any book on fractals I have read, this is by far the most beautiful.I really liked this book, so much I donated it to the library of my alma mater.

Patterns to Inspire - A Captivating Look into Fractals
This book brings a comprehensive and visually intriguing approach to the study of fractal geometry and the chaos theory. Through thought provoking imagery and discernible explanations & comparisons, John Briggs has sparked my curiosity where I now look more closely at the world around me. I believe this book is intended to captivate those with the ability to visualize and appreciate the aesthetics and interconnectedness of the arts, sciences and the natural phenomena that surrounds us. An insightful & visually stimulating read!

Don't buy this book
This book says absolutely nothing.It has a few good pictures (the best one is one the cover by the way), but the text is utterly worthless and uninformative.My favorite quote from the book is "Nonlinear means not linear."Really?Don't waste your money.Now I understand why I found it at the used bookstore.

Great Photos, Poor Content
This is a fantastic source of images on the subject of fractals, but not a great source of learning. Most books on math and science are difficult for the general reader; few authors (like Isaac Asimov) can make complex things easily understood. But the author of this book is, in my opinion, doing the public a disservice by oversimplifying the subject. The explanations underestimate the public's ability to think, and even include a number of things which are either dead wrong or made-up! The subject of fractals is still new, and there are recently more books available to explain fractals to the general public. Again, this is a great source of images, if that's what you're looking for, but look for another source if you want to undersatnd and appreciate this incredible and important topic. ... Read more

Product Description
Published in cooperation with the National Council of Teachers of Mathematics, this text is based on lectures given to various communities of teachers and students. Written especially for teachers and intended for classroom use at high school and college levels, the book also can be used for independent study. ... Read more

Customer Reviews (1)

Fractals for the Classroom
Actually, this is a pretty good book, but if you are seeking a simple way to understand and begin to understand Fractals, this book still require a good amount of math knowledge.I have yet to find a cogent, simple book for the curious, but not math minded that is not so "dumbed" down to the point of just showing pretty pictures. ... Read more

Product Description

Fractal geometry is the formal study of mathematical shapes that display a progression of never-ending, self-similar, meandering detail from large to small scales. It has the descriptive power to capture, explain, and enhance one's appreciation of and control over complex diversity. Natural shapes and rhythms, such as leaves, tree branching, mountain ridges, flood levels of a river, wave patterns, and nerve impulses, display this cascading behaviour. These fractal concepts are found in many fields, from physics to musical composition.
Architecture and design, concerned with control over rhythm, and with such fractal concepts as the progression of forms from a distant view down to the intimate details, can benefit from the use of this relatively new mathematical tool. Fractal geometry is a rare example of a technology that reaches into the core of design composition, allowing the architect or designer to express a complex understanding of nature.
The exposition of the book is at a level suitable for applied scientists, architects, and students with a modest background in mathematics. It is well illustrated and has numerous examples from which to learn the underlying concepts and their applications. Thus the book is addressed to a wide audience with a multiplicity of interests in new compositional ideas.

Customer Reviews (1)

Only book I've seen that understands both subjects
Bovill does a good job of explaining the principles of fractal geometry in layman's terms for those not already familiar with them. I was particularly impressed with his understanding of how fractal dimension varies with scaleand which scales are important for architecture. However, I wasdisappointed that there were no references made to structural properties offractals and how they might have excellent strength to weight ratios for awide range of scales. Everything was taken from a design perspectiveconcerned with texture. ... Read more

Product Description
Everything You’ll Need to Create Thousands of Fractals!

Fractals are the name given to certain types of iterated equations that produce very strange results and are capable of creating unusual and beautiful patterns. Creating Fractals describes the characteristics and mathematical background of fractals and shows the reader how the accompanying fractal-generating program is used to produce thousands of different kinds of fractals, to enlarge them, to color them, and to save them—without any knowledge of computers or programming. The program works with any computer using Windows. In addition to producing artistic effects, the reader can gain an understanding of how each type of fractal is created and how it might be used to treat natural phenomena, e.g., the turbulence of liquids, the behavior of the stock market, and the compression of graphic images. Mathematical terminology is explained in elementary terms.

KEY FEATURES:* Includes a fractal-generating program on the CD-ROM that is capable of producing and modifying thousands of fractals* Describes the mathematics (in elementary terms) involved in creating different types of fractals* The CD-ROM has over 100 example fractal images and includes all of their source code, permitting modification of the program to add new fractals, or change the program to meet specialized requirements ... Read more

Customer Reviews (4)

Creating Fractals
The software included inthis book is retro 20 century, lame.
Images are strictly low-res (600x400); interface pedantic: no retrace, wouldn't save bmp images on XP. wasted money!

Disappointing book creates but does not teach fractals
I really expected better from Roger Stevens. In the past he has written some truly excellent books on computer graphics that included working code. This particular book is very elementary with only the bare bones of the mathematics of fractals being given. Most of the book just shows a picture of each type of fractal covered, a screenshot of the included application and what you should type into the application to get the resulting fractal, and some text without equations on each fractal. If you really want to learn the mathematics behind fractals you should read "Chaos and Fractals" by Peitgen, and the older "Science of Fractal Images" by the same author. Both books are accessible yet go into sufficient mathematic detail that you could write working code. The authors even offer up code examples of their own. The second book I mentioned on fractal imaging has some great code samples and mathematics for creating beautiful realistic natural scenes of forests and lakes that are completely computer generated. I notice Amazon does not show the table of contents so I do that here:
1.Introduction
2.What are Fractals?
3.The Lorenz and Other Strange Attractors
4.What you can do with L-System Fractals
5.The Snow Flake and other Von Koch Curves
6.Peano Curve
7.Generators with Different Sized Line Segments
8.The Hilbert Curve
9.FASS Curves
10. Trees
11. Creating your own L-System Fractals
12. Newton's Method
13. What you can do with Mandelbrot-Like and Julia-Like Fractals
14. The Mandelbrot and Julia Sets
15. Working With Colors
16. Fractals with the Logistic Equation
17. Fractals using Transcendental Functions
18. Fractals using Orthogonal Polynomials
19. Creating your own 2nd-order to 7th-order Equations
20. Phoenix Curves
21. The Mandela and Pokorny Fractals
22. Fractals Using Circles
23. Barnsley Fractals
24. Iterated Function Systems
25. Midpoint Displacement Fractals

Dissaponted
I got this book to learn how to generate fractals and use the included programm to generate large images for printing. While the programm is very flexible in terms of what it generates, maximum resolution is something like 600x400. There are better books that bescribe what fractals are. This book will not help you to set up calculations on you own and it's fractal generation programm is useless for anything other that on screen display.

Introducing the Mathematics of Fractals
Fractals were originally considered to be a rather messy offshoot of conventional mathematics. They required entirely too much arithmetic to be useful before the age of computers. But with computers the whole concept of fractals became something that could indeed be studied.

A bit of time goes by and all of a sudden the people doing fractals begin to discover that using the right kind of mathematics can be used to produce a lot of images that begin to look like things in nature. These drawings began to look like things such as trees, mountains, clouds, explosions. And all of a sudden there was an interest beyond those of the mathematician just drawing cute geometric patterns, it's called game development.

This book is not on gaming, it's on the basics of fracticals. It includes software to generate fractals, and it gives the mathematics of how these fractals are created. It's a basic, beginners book to computer graphics at the mathematical level. ... Read more

Product Description
The first book to discuss fractals solely from the point of view of computer graphics, this work includes an introduction to the basic axioms of fractals and their applications in the natural sciences, a survey of random fractals together with many pseudocodes for selected algorithms, an introduction into fantastic fractals such as the Mandelbrot set and the Julia sets, together with a detailed discussion of algorithms and fractal modeling of real world objects. 142 illustrations in 277 parts. 39 color plates. ... Read more

Customer Reviews (4)

Fractals -- Applied Mathmatics and Computer Programming
From page 25" Fractals (a word coined by Mandelbrot in 1975) have blossomed tremendously in the past few years (written in 1988) and have helped reconnect pure mathematics research with both the natural sciences and computing."

This book has both Mathmatical equations and Computer Programs along with explanations and results (many graphs, plots, and color plate images).

If you have an interest in Fractals, Recursion, Computer programming, Image creation, this is a great book and filled with examples.

Great book on fractals and imaging
This old book is a timeless gem. It goes into the details of the mathematics of fractals and also shows well-commented C code for producing fractal imagery along with good color illustrations.
Chapter 1, "Fractals in Nature", uses computer generated images to build a visual intuition for fractal as opposed to Euclidian shapes. There is also a mathematical characterization with Brownian motion as the prototype.
In chapter 2, "Random Fractal Algorithms", randomness is introduced into the algorithms discussed in chapter one as a way of simulating natural phenomena. Ideas are extended to higher dimensions. C programs that produce mountain ranges using these ideas are presented, along with the resulting imagery.
Chapter 3, "Fractal Patterns Arising in Chaotic Dynamical Systems", turns to the topic of dynamical systems and is less mathematical than the first two chapters. There is some mathematics and some illustrations in 2D and black and white that should be familiar to any student of dynamical systems.
Chapter 4, "Fantastic Deterministic Fractals", demonstrates how genuine mathematical research experiments open a door to a new reservoir of fantastic shapes and images. Programs are shown that extend the ideas of chapter 3 into truly beautiful fractals. Ideas here stay mainly in 2D.
The final chapter, "Fractal Modelling of Real World Images", draws from the material of the previous chapters to present C programs that produce clouds, vegetation, smoke, and mountain ranges, all by altering a few of the parameters in the sample code presented by the authors.
This book is much better than more recent titles that bury their algorithms in complex high level languages or "toy books" on the subject that provide dumbed-down applications and in which the simplest possible explanation of fractals is given with no insight. I highly recommend this book to anyone interested in understanding fractal mathematics and in using that mathematics to produce stunning visual effects.

One of the best (if no the best) in the feild
You cant go past this book,

This book reads at any level, Great introduction to the field as well as an indespencible reference. Shows easy to implement code examples, and has lots of pictures showing what can beacheived.

This has been a main reference for a theisis I am currentlyworking on. The question is, why is it out of print. If you can find itit's worth it's wheight in gold.

A must
In my opinion, the best work ever written in the category not-for-beginner-but-available-to-non-specialist (such as Beauty of Fractals, by the same authors). An easy answer to question "How can Igenerate a fractal image with my PC?", from brownian motion to Juliasets. A must for reader interested in fractals (a bit out-of-fashion butstill very interesting field). ... Read more

Product Description
Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics.It has become a new tool for modeling in biology, geology, and other natural sciences.

Anthropologists have observed that the patterns produced in differentcultures can be characterized by specific design themes.In Europeand America, we often see cities laid out in a grid pattern ofstraight streets and right-angle corners.In contrast, traditionalAfrican settlements tend to use fractal structure--circles of circlesof circular dwellings, rectangular walls enclosing ever-smallerrectangles, and streets in which broad avenues branch down to tinyfootpaths with striking geometric repetition.These indigenousfractals are not limited to architecture; their recursive patternsecho throughout many disparate African designs and knowledge systems.

Drawing on interviews with African designers, artists, and scientists,Ron Eglash investigates fractals in African architecture, traditionalhairstyling, textiles, sculpture, painting, carving, metalwork,religion, games, practical craft, quantitative technologies, andsymbolic systems.He also examines the political and socialimplications of the existence of African fractal geometry.His bookmakes a unique contribution to the study of mathematics, Africanculture, anthropology, and computer simulations. ... Read more

Customer Reviews (7)

Former Student
I had Ron Eglash as a professor at Rensselaer Polytechnic Institute. Discussing and analyzing aspects of this book, including self-organization in general, was very interesting and valuable to say the least. The book makes no assumptions in knowledge and will cleanly bring in the topic of fractals in african culture. I had read the book the winter break before taking the course and had no difficulty understanding the material even as a freshman. The concept is quite intriguing and shatters many of the held perceptions of "the hierarchy of mathematics." Ron Eglash is a great man and I know he loves talking with people that share similar interests in mathematics or cybernetics.

At times the author crosses the line where mathematics is "found" inside situations when it is not there
This book can be placed in the category of ethnomathematics, where the emphasis is on the ethno rather than the mathematics. Fractals are by definition structures that are self-similar over a large number of iterations and scales of measure. If you accept that only a few iterations are sufficient to define a fractal, then the structures described in this book can be considered fractals. However, the author does the best job of summing up the content in the first two sentences of chapter 11.

"Parts I and II of this book emphasized the geometric, symbolic, and quantitative aspects of African fractals. Some cases were more speculative than others - a difference that I hope was clearly indicated - but even in the use of mythic narrative, I generally restrained conclusions to those that had geometric or quantitative counterparts."

I agree that the author generally stayed within the bounds of reasonableness in describing what are called fractal structures in African design, but only if you stay within the bounds of a few iterations of shrinking self-similarity being sufficient to have a structure be considered a fractal.
In the last four chapters, the author makes some points that are both revealing and questionable. On page 182, after pointing out that anthropologists need years of study to understand a culture the author states, "My thin description fieldwork lasted only a year and moved through Senegal, Mali, Burkina Faso, The Gambia, Cameroon, Benin and Ghana." By his own admission, Eglash is not qualified to speak to deep cultural issues, yet he proceeds to do so. The section that begins on page 209 with the title "Recursion and sex - a cross-cultural comparison" simply went way beyond or more precisely out of my understanding of fractals, recursion and sex. I did not understand either the statement "This section will focus on the relation between recursion in mathematics and sexuality in culture" or the purported explanation.
While I am a strong supporter of the concept of ethnomathematics, people writing in support of it must take great care not to avoid finding mathematical ideas or intent inside situations where none exist. In my opinion, Eglash crosses that line in this book.

Published in Journal of Recreational Mathematics, reprinted with permission,

a good introduction to African mathematics and fractal geometry
This book starts out with a presentation of fractal geometry which is very comprehensible and enjoyable. Next it covers specific aspects of fractal geometry and their relation to African society, architecture, fashion, art, divination and games. This part of the book is very fascinating. I learned a lot about how recursion works and how it is used in African buildings and fashions in the chapter on recursion. Other chapters in this section are Geometric algorithms, Scaling, Numeric systems, Infinity and Complexity. They are all very interesting. The final section is on the implications of the fact that Africans used this kind of mathematics. The author emphasizes the application of African fractal geometry to education especially the education of African Americans who sometimes feel alienated from math classes which focus on the achievements of European peoples. One thing that the author stresses is that the fractal designs of, say city planning, made by African peoples are not more "natural" than the Western approach of dividing cities into rectangles. He says this assumption dovetails into a preconception of African societies as being somehow closer to nature and therefore unsophisticated. The author points out that fractal mathematics is hardly simple and also not easily intuited either. I did not find myself making this assumption but apparently some people do fall into this trap. Anyway, I highly recommend this book to anyone wanting an introduction, with applications, to fractal geometry and its use in African societies. I also recommend this book to educators looking for a way to get their students, regardless of their background, to be more interested in mathematics.

Connecting Africans ancient and modern
This is an amazing book! It clearly shows how many of the common things that people of African descent do have may scientific connections.Hair styles that are worn today by people of African descent, have been worn as far back to the ancient indigenous Africans known as the ancient Egyptians.So it really no surprise that there is mathematical and scientific knowledge being found today by scientist and scholars.

This book should be in every school and home in this country.I take that back, this book should be in every school globally.

Another scientific book that would make a great set for any school or home is, The African Unconscious.Written by Edward Bruce Bynum.You can find it here on Amazon.com.

This book helps to render obsolete long-held myths.
Ron Eglash's brilliant work on Afrikan fractals helps to shatter long-held myths and misconceptions about Afrikans, the most pervasive and pernicious of which is the notion of Afrikans (both on the Motherland and in the Diaspora) as inactive agents in history. This work motivated me to complete mine on chaos theory and Afrikan fractals. My longer reviews of Eglash's book appear in the Nexus Network Journal (vol. 2, 2000:165-168) and the Journal of Third World Studies (vol. xviii, no. 1, 2001:237-239), each reflecting the publication's genre and disciplinary focus. Dr. Abdul Karim Bangura is a researcher-in-residence at the Center for Global Peace and a professor of International Relations in the School of International Service at American University, and the director of The African Institution in Washington, DC. He is the author of 21 books and more than 200 scholarly articles. ... Read more

Product Description
For almost 15 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 this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot Set, Julia Sets, Cellulair 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 images and compression; the second, by Carl J.G. Evertsz and Benoit Mandelbrot, introduces the foundations and implications of multifractals.Amazon.com Review
Fascinating and authoritative, Chaos and Fractals: NewFrontiers of Science is a truly remarkable book that documentsrecent discoveries in chaos theory with plenty of mathematical detail,but without alienating the general reader. In all, this text offers anextremely rich and engaging tour of this quite revolutionary branch ofmathematical research.

The most appealing aspect about Chaos andFractals has to be its hundreds of images and graphics (withdozens in full-color) used to illustrate key concepts. Even themath-averse reader should be able to follow the basic presentation ofchaos and fractals here. Since fractals often mimic natural shapessuch as mountains, plants, and other biological forms, they lendthemselves especially well to visual representation.

Early chaptershere document the mathematical oddities (or "monsters") such as theSierpinski Gasket and the Koch Curve, which laid the groundwork forlater discoveries in fractals. The book does a fine job of placingrecent discoveries about chaos into a tradition of earliermathematical research. Its description of the work of mathematicianslike Pascal, Kepler, Poincaré, Sierpinski, Koch, and Mandelbrotmakes for a fine read, a detective story that ends with the discoveryof order in chaos. (For programmers, the authors provide shortalgorithms and BASIC code, which lets you try out plotting variousfractals on your own.)

This is not, however, only a book of prettypictures. For the reader who needs the mathematics behind chaostheory, the authors in no way dumb down the details. (But because thericher mathematical material is set off from the main text, thegeneral reader can still make headway without getting lost.)

Therehave been advances in the field since this book's publication in 1992,but Chaos and Fractals remains an authoritative generalreference on chaos theory and fractals. A must for math students (andmath enthusiasts), Chaos and Fractals also deserves a place onthe bookshelf of any general reader or programmer who wants tounderstand how today's mathematicians and scientists make sense of ourworld using chaos theory. --Richard Dragan

Topicscovered: Overview of fractals and chaos theory, feedback andmultiple reduction copy machines (MRCMs), the Cantor Set, theSierpinski Gasket and Carpet, the Pascal Triangle, the Koch Curve,Julia Sets, similarity, measuring fractal curves, fractal dimensions,transformations and contraction mapping, image compression, chaosgames, fractals and nature, L-systems, cellular automata basics,attractors and strange attractors, Henon's Attractor, Rössler andLorenz Attractors, randomness in fractals, the Brownian motion,fractal landscapes, sensitivity and periodic points, complexarithmetic basics, the Mandelbrot Set, and multifractal measures. ... Read more

Customer Reviews (13)

This book is a dream come true.
This book is a dream come true.
No other publication comes close to such complete coverage of the subject.
It is highly readable even for a novice like myself.
It has been a great joy to me.
Many thanks to the authors for doing such a great job.

It's all true: Best single source on fractals-but get the 1st ed.
Thanks to S.J. Will for the tip: Get the FIRST edition (used), as I did and save more than half the price, even of a used copy of this newer edition. Can't compare the two (having not seen the new one) but I can say the color images are very sharp in the older book. As far as content, I too have looked at and bought several books trying to understand fractals. (I am not math-literate, beyond high school algebra.) I found this book most helpful, but NOT easy for the general reader, beyond the first few, introductory pages. As other reviewers have noted, most of it is WAYYYY over the head of anyone who's not a college math major, but skipping through the examples and exercises (some of which are very rewarding if you can stay with it), I found the general explanations, the excitement of the authors, the broader significance of fractals all to be well-worth the price. -- And hey: at over 900 pages ( ! ) and with FORTY color plates, this book is an astounding bargain. Strongly recommended, even for novices.

"The Colors of Infinity," based on the video documentary by Arthur C. Clarke is a good introduction to fractals. An enjoyable DVD is included of the original TV program, especially if you learn better by watching and listening. The accompanying animated fractals are fascinating, but frustratingly poor resolution. For a more philosophical approach to fractals, I highly recommend "Heaven's Fractal Net" by William Jackson.

Compare the editions
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.

Excellent tutorial on nonlinearity
At least 50% of this book can be well understood by any 1st year, exact science student. There are a couple of mathematical issues that are more senior-like, but never mind. With the appropriate teaching or guidance, a lot of practical, advanced tasks can be tackled down.I could use this book all along for giving examples for college (university), undergraduate students of almost every mathematical subject: numerical analysis, calculus, linear algebra, group theory, algorithm theory, visualization in 2 and 3 dimensions, topology...you name it, after reading this book. No fuzzy theory or wavelets or any other advanced statistical method for dynamical systems is formally mentioned, though. However the concept of measure is very well introduced and described with examples. For physics is not bad for dynamical systems theory. Although no Hamiltonian or Lagrangian formalism is mentioned, the description on how to obtain Lyapunov exponents out of a set of differential equations is very good. Engineers get their share too: useful examples are given about, e.g., feedback and control theory (mind you, it is not a book specialized in, say, robotic control using chaos theory, but it is a good start). For philosophers and the layman there are quite a few pages as well. The foreword from Mitchel Feigenbaum, just to give an example, tells us a kind of summary which "warms up" the reader and "exorcises away" the possible fantasies an unprepared reader could have regarding (or against or in favor of) the word "chaos". Nice color plates for those with artistic inclinations and the graphics are just so very well printed, you can practically "follow" their computation. Not a bad book at all for your personal (or institutional) library, I may say.

A good introduction
Chaos as a physical theory began essentially in the 1970's, but as a mathematical field it has existed since the early 1900's. This book covers only the mathematical study of chaos, and is addressed to those readers who have a fairly strong background in undergraduate mathematics. A knowledge of dynamical systems and measure theory would help in the appreciation of the book, but are not absolutely necessary. The application of fractals and chaos to finance is now legendary, but other applications, such as to packet networks and surface physics are not so well-known. Current research in chaos is done predominantly in the context of information theory, wherein the goal is to understand the difference between chaos and noise, and develop mathematical tools to quantify this difference. The BASIC code in the book gives away its age, but can be easily translated to one of the symbolic computing languages available now, such as Maple or Mathematica.

This is a sizable book, and space prohibits a detailed review, but some of the more interesting discussions in it include: 1. The video feedback experiment, which can be done with only a video camera and a TV set. This is always a crowd pleaser, at whatever level of the audience it is presented to. 2. The comparison between doing iteration of a chaotic map on two different calculating machines: a CASIO and an HP. The difference is very dramatic, illustrating the effect of finite accuracy arithmetic. 3. The pictures illustrating the Chinese arithmetic triangle and Pascal's triangle as it appeared in Japan in 1781. 4. The space-filling curve and its relation to the problem of defining dimension from a topological standpoint. This discussion motivates the idea of covering dimension, which the authors overview with great clarity. They also give a rigorous definition of the Hausdorff dimension and discuss its differences with the box counting dimension. 5. The many excellent color plates in the book, especially the one illustrating a cast of the venous and arterial system of a child's kidney. 6. The difficulty in measuring power laws in practice. 7. Image encoding using iterated function systems, which has become very important recently in satellite image analysis. This leads into a discussion of the Hausdorff distance, which is of enormous importance not only in the study of fractals but also in general topology: the famous hyperspaces of closed sets in a metric space. 8. The relation between chaos and randomness, discussed by the authors in the context of the "chaos game." 9. L-systems, which are motivated with a model of cell division. 10. the number theory behind Pascal's triangle. 11. The simulation of Brownian motion. 12. The Lyapunov exponent for smooth transformations. 13. The property of ergodicity and mixing for transformations, the authors pointing out that true ergodic behavior cannot be obtained in a computer where only a a finite collection of numbers is representable. 13. The concept of topological conjugacy. 14. The existence of homoclinic points in a dynamical system. These are very important in physical applications of chaos. 15. The Rossler attractor and its pictorial representation. 16. How to calculate the dimensions of strange attractors. 17. How to calculate Lyapunov exponents from time series, which is of great interest in many different applications, especially finance. 18. The Julia set, which the authors relate eventually to potential theory. ... Read more

Product Description
This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers.While keeping the mathematics to a simple level with few formulas, the reader is introduced to an area of current scientific research that was scarcely possible until the availability of computers. The book is divided into two main parts; the first provides the most interesting problems, each with a solution in a computer program format. Numerous exercises enable the reader to conduct his or her own experimental work. The second part provides sample programs for specific machine and operating systems; details refer to IBM-PC with MS-DOS and Turbo-Pascal, UNIX 42BSD with Berkeley Pascal and C.Other implementations of the graphics routines are given for the Apple Macintosh, Apple IIE and IIGS and Atari ST. ... Read more

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University of Washington, Seattle.Physiological research on fractals and chaos. Fractals are objects or processes with multiple-scale properties. For physiologists or mathematicians. ... Read more

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The Fractal Geometry ofNature is a mathematics text. But buried in the deltas and lambdasand integrals, even a layperson can pick out and appreciateMandelbrot's point: that somewhere in mathematics, there is anexplanation for nature. It is not a coincidence that fractal math isso good at generating images of cliffs and shorelines and capillarybeds. ... Read more

Customer Reviews (20)

A great insight into the world of fractals
This is a great book for someone looking to discover what all the hullabaloo is about fractals.It provides a wonderful insight into the mind of one of the great mathematical geniuses of our time, Benoit Mandelbrot.I think some people will find his writing style a bit too stodgy, almost arithmetical, but I find it interesting.I especially appreciate how marks off when he's going to be tangential with special brackets.Mandelbrot doesn't delve into too many rigorous mathematical proofs of the various topics he discusses.He broaches each subject in such a way that should be accessible to people from a wide array of sciences and disciplines.I don't recommend this book if you're trying to figure out how to create simple fractal programs.But I enthusiastically recommend it if you want to learn more about fractals, discover a new way to think about and understand nature, or are simply looking for a good bit of erudition.

A fractal is by definition
A set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.

The definition of a fractal pretty much sets the tone for the book. There are mostly definitions and monochrome diagrams to explain the more classical fractals. The book does shows some practical geometric uses for fractals but I would not let it get anywhere near my Koch Curve.

I am not being kind to this book as there is a color section in the center. That shows "The Great Wave" by Katsushika Hokusai (1760-12849.) And an extensive reference section.

The book its self could easily be used as a text book for school.

Fractals: Hunting the Hidden Dimension (Blu-ray) [Blu-ray]

An Eye For Fractals: A Graphic And Photographic Essay (Studies in Nonlinearity)

How We Mandel
This book is the latest version of a book the famous Benoit Mandelbrot wrote back in the mid-1970s, in which he coined the term "fractal". The subsequent version was released around 1980 and had, among other pictures, a black blotchy image on a white background which he called "the µ-map". Then some joker started calling it "The Mandelbrot Set" and he had to change the book again.

It is true that this is not the best-written book on fractal geometry. However, for a time it was the ONLY book on fractal geometry, and as such has incredible historic value. Imagine in ancient Greece where people had to borrow one of Euclid's latest scrolls to read about things found in no other work.

Personally, this book has taught me only a few things. I had already learned about fractals from articles in 1980s issues of Scientific American, and computer programs in Compute! magazine.

Many black-and-white images suffuse this tome, though there are some color plates which are by no means as complex as today's fractallographies, but will serve as an introduction to the genre.

The only Mandelbrot Set image is the blotchy one mentioned earlier. That's because Dr. Mandelbrot, though he discovered the set, wasn't the first to color the complement, and it was Heinz-Otto Peitgen's 1984 book "The Beauty of Fractals" that has the first color Mandelbrot pictures.

I wholeheartedly recommend this book for a glimpse into history, and the uninitiated may learn something as well; though I wouldn't demand that much of it.

A fractal is by definition
A set for which the Hausdorff Besicovitch dimension strictly exceeds the topological dimension.

The definition of a fractal pretty much sets the tone for the book. There are mostly definitions and monochrome diagrams to explain the more classical fractals. The book does shows some practical geometric uses for fractals but I would not let it get anywhere near my Koch Curve.

I am not being kind to this book as there is a color section in the center. That shows "The Great Wave" by Katsushika Hokusai (1760-12849.) And an extensive reference section.

The book its self could easily be used as a text book for school.

Fractals: Hunting the Hidden Dimension (Blu-ray) [Blu-ray]

An Eye For Fractals: A Graphic And Photographic Essay (Studies in Nonlinearity)

item as promised
it took a long time to get to me but it was delivered as descibed, great condition... good seller ... Read more

Product Description
This volume contains the proceedings of the first IFIP conference on fractals. The mathematical concept of fractal was coined by B.B. Mandelbrot in the early seventies to characterize objects with self-similar structures at all levels. Now the field of fractals is being subject to intensive research and an extensive growth of applications in many sciences. This first IFIP conference, intended as a start of periodic conferences on fractals, enables a productive cross fertilization of ideas among specialists in fractals and in information processing. In addition to the volume's 44 colour illustrations, on page v is a rare view of fractals and the Portuguese architecture at the time of the navigators, produced by Master Lima de Freitas, a leading Portuguese artist and member of the conference organizing committee. The design illustrates the symbiosis of mathematics and human artifacts represented by the real world. ... Read more

Product Description
Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century. Penetration of the resulting new paradigms into practically all academic disciplines has confirmed the fundamental assertion of universal formalism common to a wide range of human endeavors.

This book contains an extended article by B B Mandelbrot, reviewing his contribution to fractal geometry and outlining some unsolved problems, with illustrations especially of finance and physics. It covers a range of multidisciplinary topics — from the biology of aging, through the self-similar shape of plants, image decompression and solar magnetic fields, to sound reflection in the street. The book is a treasure trove for innovative researchers working in fields related to fractal geometry. ... Read more

Product Description
Simple mathematical formulas are transformed intostrikingly beautiful computer generated designs. The dynamic interplaybetween order and chaos is explored in 350 color images in this uniquecoffee table book that explains the mechanics of mathematicalart. Berkowitz is perhaps the world's most widely recognized fractalartist. Fractal Cosmos is the first art book to feature fractalimagery and the largest collection of fractal art published anywhere. ... Read more

Customer Reviews (6)

333 color plates, graphical potential of fractals, album-like
This unique album-like beautifully published on 212 pages of glossy paper includes 333 color plates of computer generated images of fractals and fractal compositions. They reveal the graphical potential of fractals and are a visual introduction to their graphical application. Most of them could be found in a smaller size on the Web using the keyword lifesmith. The book's text is concise and includes a step-by-step explanation that extends from a typical school knowledge. Its simple instructions allow to recreate the fractals on computer. The whole content is easily accessible to non-experts, and it is good even for just casual browsing through. The book comprises an introduction to fractals on 4 pages; 5 chapters of images with a different type of fractals and one page description in each; 4 appendices dedicated to generating fractals (5 pages), bibliography (2 pages), formulae (1), and fractal data for each plate except the compositions (47 pages); and an index of equations on 5 pages.
TABLE OF CONTENTS
Preface vii
Acknowledgments ix
CHAPTER ONE
Introduction to Fractals 1-1
CHAPTER TWO
Mandeibrot/Julia Set Fractals of the Equation f(z) = z2 + c 2-1
CHAPTER THREE
Mandeibrot/Julia Set Fractals of Polynomials, Powers,
Roots, and Rational Expressions 3-1
CHAPTER FOUR
Mandeibrot/Julia Set Fractals of Exponentials, Logarithms,
Trigonometrics, and Combinations Thereof 4-1
CHAPTER FIVE
Three-Dimensional Fractal Compositions 5-1
CHAPTER SIX
Special Image Studies in Fractals 6-1
APPENDIX A
Generating Julia Set Fractals A-1
APPENDIX B
Selected Bibliography B-1
APPENDIX C
Important Formulae for Complex Numbers C-1
APPENDIX D
Supplemental Fractal Data for Color Plates D-1
INDEX BY EQUATION I-1

Great intro to fractals
There's not a lot of easily understandable information, but WOW!The pictures are great!

math and art
This is a cool book. I tutor middle school students in math and have used this to help them think outside the box. Math can be used to describe everything around us. This book has beautiful color photos of unique calculus graphs.The kids are amazed by the beauty of these designs.

A fractal survey with beauty, intrigue and educational value
I'm really pleased with this book. To me, this is the IDEAL coffee table book on fractals.

Chapter one is the obligatory brief history of fractal image generation, including Mandelbrot, population growth, and citing quite a few popular books on the subject.

The heart of the book is the eye candy, presented in bright colors on high quality paper, with a bare minimum of mathematical labeling to maximize the "art appreciation" aspect of the viewing. This is divided into 5 chapters of somewhat like families of fractals, with brief but informative introductions. If you want a lot of beautiful fractal images that vary widely - you'll certainly get that here.

Chapter 2 gives many images of the Mandelbrot set. Chapter 3 explores various polynomials, powers, roots, and rational expressions. This clearly answered my early layman's question "What about other types of simple equations?" Chapter 4 then goes into exponentials, logarithms, trigonometrics, and various combinations. Chapter 5 then shows 3-d compositions, with many fractal skies, mountains, trees, and landscapes, plus the fractal spheres looking so much like moons or planets. Finally, chapter 6 does some interesting "studies" where you get treated to a page at a time of (6) images with very similar equations, where he alters some variable. Examples: the amount of zooming (up to 169 quintillion - with little loss in image detail), or iterating c by small amounts (like .005 to .01).

At this point I thought - very nice book, but I felt a little let down by so little INFORMATION passed along about WHAT these pictures were. The appendices changed all that!

Appendix A gives a nice explanation, complete with examples and graphs, of how to generate Julia Set fractal images. Appendix B is a 2 page selected bibliography, including both books and papers.

Appendix C lists and briefly explains 20 "Important Formulae for Complex Numbers". Having this would have saved me buying a book about complex numbers when I first discovered fractals, since it implies what the "rules" are.

Appendix D is REALLY KEY - for chapters 1-4, it lists nice mathematical data, and in almost all cases this includes: the image type, the equation, the complex constant, the screen parms, the blowup parms, and the maximum number of iterations. Here then, is HOW these beauties were created. For chapter 5, he doesn't list this, and for chapter 6, since they're studies, the detail varies, but is pretty good overall. To me, this takes the book from "very nice" to "awesome" because the layman can now get a better grasp on things and pursue what interests him/her.

Finally, unlabeled, but apparently Appendix E in my mind, he provides and index to the images BY EQUATION. A very nice cross reference to those thinking of exploring further in the literature or on their PC's.

So the "heavy math" type likely won't find much new here. For the rest of us, who just want some art, some (layman's)meaning/education, or both, aside from parts of "The Beauty of Fractals" this was without peer.

An excellent picture of fractals the CHAOS universe
Jeff, have you read of Dr. John Hubbard from Cornell and his analysis of the Mandelbrot Set? Your results and his analysis are so-ooo intriguing on what fractals promises for the future of mankind!!!!I have a video of his work and it is so fascinating. ... Read more

Product Description
This book covers analysis on fractals, a developing area of mathematics that focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals. ... Read more

Customer Reviews (1)

Metrics, fractals, analysis...
Fractals make headlines from time to time[--are they everywhere?], and and they make beautiful color pictures; but they are also part of a substantial mathematical theory, even one with an exciting mathematical history. This lovely book presents the subject elegantly in a way that it can be taught to students. It starts with the basics, then systematically, step by step, it builds up the central results. Great for the classrom, or for selfstudy! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. Example: By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. Compared to other books at the same level, for example, by Falconer, 1990, and the equally attractive one from 1985[Falconer: The geometry of fractal sets], Kigami's book stresses the analysis of the Laplace operator. Falconer covers the theory more generally, and his books have a slightly more potential theoretic bent. ... Read more

Product Description
'Interesting, informative, and clearly written. It is well andamply illustrated...The computer discs provide entertainingillustrationsand exercises...a good, solid presentation of a useful,interesting,ubiquitous subject.' --Mathematical ReviewsThe authorintegrates discussions of fractal geometry, surfacemodelingtechniques, and applications to real world problems toprovide acomprehensive, accessible overview of the field. His workwill equipresearchers with the basic tools for measurement andinterpretationof data, stimulating more work on these problems and,perhaps,leading to an understanding of the reasons that Nature hasadoptedthis geometry to shape much of our world. ... Read more

Customer Reviews (1)

Happy with vendor and product
The book was in very good condition, as stated by the vendor. It arrived promptly, and the vendor was also very helpful in seeking the companion diskette that comes with the book. This vendor earned my trust. ... Read more

Product Description
Written for mathematicians, engineers, researchers in experimental science, and anyone interested in fractals, this book presents the fundamentals of curve analysis with a new and clear introduction to fractal dimension. It explains the geometrical and analytical properties of trajectories, aggregate contours, geographical coastlines, profiles of rough surfaces, and other curves of finite and fractal length. The approach is through precise definitions from which properties are deduced and applications and computational methods are derived. Written without the traditional heavy symbolism of mathematics texts, this book requires two years of calculus as a prerequisite to understanding. This text also contains material appropriate for graduate coursework in curve analysis and/or fractal dimension. ... Read more

Product Description
This text will be a valuable tool and reference work for all those interested in fractal forms and their properties. The past decade has seen an almost exponential amount of work done in the field of non-integral dimensions. Upon publication of Mandelbrot's Objets Fractals (1975), a great number of researchers understood the interest of fractals. Many tried, by means of the theory, to set up immediately useable tools, including the author, who opted for an experimental approach and developed instrumentation to explore the widest possible range in both time and space (time resolution of the laser spectroscopy of biomolecules). In this spirit, these expert researchers organized monthly ``Hausdorff seminars on the notion of non-integral dimension and its applications'' to tackle the problems confronting practical scientists. This work captures, with many illustrative examples, the main themes of each session. ... Read more

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Customer Reviews (4)

Science and art, together again
I was aware of fractals for some time and after watching a NOVA film "Hunting the Hidden Dimension" (2008). I went hunting for some of the many books by Benoit Mandelbrot. You can imagine my surprise with I tripped over this book, "An Eye for Fractals" by Michael McGuire.

Stacked up against other fractal works, this book has more stunning pictures both in quantity and quality. Even though the formulas are a tad complex with number lines and complex planes, the ideas on how to make and see fractals are quite clear.

If we were not enamored with fractal the book would stand on its own as great monochrome depictions of nature and monuments. There is one picture by Ansel Adams and the rest are by M McGuire. If you did not see the titles I challenge you to find the Adams picture.

Every time I read this book I get a different insight into the world of fractals and believe you will also.

Fractals: Hunting the Hidden Dimension (Blu-ray) [Blu-ray]

A good primer on fractals and an excellent introduction to their appearance in nature
Looking around in nature, it is easy to find examples of fractals. Individual plants, forests, volcanic activity, wind and water erosion, the flow of water and the movement of plants with the wind can all be described by an appropriate fractal function. Most of the pages of this book are taken up with spectacular images of such natural fractals. A few of the pages are devoted to the mathematical background used to generate the images. It is not rigorous; it was the author's intention to only give some of the general ideas rather than a complete description. They are understandable, even if your math background stops at algebra. Although it was written in 1991, this book is still an excellent primer on what fractals are as well as the large number of ways that they appear in nature.

beautiful BW photographs
I just got this book from the library. It many well printed BW photographs. There is some math discussion on fractals but there is no discussion of computer software for generating fractals pictures. Still a great book.

A beautiful journey through math and nature
One of the only fractal books available for non-mathematicians, An Eye forFractals interweaves beautiful photographs of natural scenes withexplanations of their fractal geometric characteristics.It gives enoughinformation about fractals for a beginner to understand what they are andhow they apply to nature.Its photography makes it a perfect book to leaveout on the coffee table.

Fractal geometry is revolutionizing the way thatscientists perceive the universe and its underlying order.Anyone canbenefit greatly from this understanding by reading this book. ... Read more

Product Description

A specialized presentation of fractal analysis oriented to the social sciences

This primer uses straightforward language to give the reader step-by-step instructions for identifying and analyzing fractal patterns and the social process that create them. By making fractals accessible to the social science students, this book has a significant impact on the understanding of human behavior.

Key Features

• Detailed examples help readers learn and understand the analytical methods presented.
• Matlab codes for programs allow users to implement, on their own, some of the techniques described in the text. Visit http://www.ccs.fau.edu/~liebovitch/larry.html for more details.
• Clear and logical explanations of fractals and their analysis enable the instructor to easily teach and the student to easily learn the material.

This is the only book designed to introduce fractal analysis to a general social science audience.

Product Description
The theory of fractals has been used to describe complicated shapes in nature, such as clouds or trees, by introducing a new quantity called the fractal dimension. This revolutionary theory has been applied in many fields and is being compared to Newton's theory of mechanics. This textbook begins with an elementary introduction to fractals, and goes on to deal with more sophisticated problems, identifying a number of examples of fractals in nature and explaining how to identify fractal patterns. Computer simulated fractals are also introduced with short programs for use on personal computers. For the more advanced reader, the text also deals with theoretical topics such as chaos, percolation, statistical models of turbulence and renormalization group methods. ... Read more