Fractal Books

Just received my new book by Marilyn. I have not had a chance to try the tutorials yet but have read quite a few chapters and am loving every minute of it. Marilyn has made the lessons very simple and straightforward. I love how she has classified the brushes and showed what each can do on painting hair.
Marilyn has also recommended some software that should be interesting to try.
I am highly recommending this book to my painter friends. As soon as all the activities of this holiday season calms down I am going to try each and every one of them.

Great Book, I have several books on Painter that I have never finished. This one is a great read, and the 1st that doesn't feel like a user's manual or a text book. Full color pictures bring the book to life. Leaves your excited to paint. I had idea after idea for different painting and it was a challenge to decide which one to start with.

I like this book so much I am buying one for a friend. I have been using Painter for several years and bought this book because I admire Marilyns work. Even though I thought I knew Painter pretty well she has taught me many things!

The book is well done with lots of photos so you can see what you are aiming for.

I am using painter 9.5 and even though it is written for X I still can do most everything in the book. I highly recommend it for anyone wanting to learn the program.

Marilyn Sholin's book is outstanding. I have every book written on Painter X and yet this book really stands out in the field. I like the easy to understand directions and the thoroughness of each lesson. the book is gorgeous to look at and motivates me to pick up my digital paintbrush once again.

The Art of Digital Photo Painting by Marilyn Sholin is a great resource for anyone new to the world of digital painting. The instructions in the book are easy to follow and she takes the time to explain processes so we aren't just doing the work, but we understand what is happening. I've wanted to learn digital painting for a while now but was intimidated by the process. Having access to her images and being able to work through the process with her instructions is SO helpful. I was even able to take information in the introduction chapters and tweak to adjust for filters as I went through some of the tutorials. Great book, if you are thinking about getting into digital painting, a MUST HAVE.

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 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.

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.

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.

I'm a part time faculty member at a Boston art school. At the school I teach a class on Digital Illustration using Painter. I myself use the Painter WOW! Book as an instructional tool, and it is actually a required text for the class. If you're at all interested in Painter, reading this book is one of the best things you can do for yourself, it's a must have! Cher's book does not just tell you how you "could" use Painter; she provides real world applications of the tools within Painter to show what you "can" do. Due to the seemingly complex interface, without this book, a new user could potentially be scared away from the application. The Painter WOW! will help you work through the entire application, progressing at your own pace. As for seasoned users, such as myself, you are sure to come away with many new tips and tricks; you'll wonder how you ever worked without them. I started buying the Painter WOW! Books back when version 5 had just been released. WOW! 6 was great, and WOW! 7 is better yet! Not only is this book chalk full of useful information, it's a visual delight. Bravo!

I love Painter--been using it since it was a simple black and white sketch program sold in an imitation cigar box years ago. But this program, which imitates art media digitally, can be a bit complicated to use.

Once you do get acquainted with the basics from the tutorial included with Painter, you can improve your layer techniques, web techniques and practice the projects in this book.

I frankly got this for the CD with extra brushes, papers, textures and stock material. But the ability to go through the examples in the book has improved my technique with Painter. If you use Painter 7 AND Photoshop, there is a chapter on combining the two. That's VERY valuable.

Highly recommended for Painter 7 users.

When I saw a recent review that said the book has only one portrait technique, I just had to point out that it has lots more than that! A quick search turned up "Sketching with Pencils" (OK, the subject is feline rather than human, but still it's a portrait, p. 64), "Drawing with Colored Pencils" (starting from a sketch, p.65), "Gouache and Opaque Watermedia" (also starting from a sketch, p. 84), "Sculpting a Portrait" (using Chalk variants, p. 88), "Oil Painting on Layers" (as the reviewer noted, p. 180), and "Cloning a Portrait" (turning a photo into a painting, p. 215). Wouldn't it be great indeed to have more detailed explanations of the pieces in the "Gallery" sections? But I'm afraid that would make the book too heavy to lift! The step-by-step detail in the techniques is great, and the "Galleries" are there to inspire us.

This book is a great asset in helping one understand and navigate the complex palettes that come with Painter 7. It really helps the artist fine tune and accomplish the desired effects for specific examples. It also discusses the various ways in which to start a painting, either from a photo, a sketch or from scratch. My only disappointment would come from the lack of details on how to achieve the truly great effects seen in the gallery images. I think this book is a wonderful tool for graphic designers like myself. But it really skims the surface on creating great works of art. I think a lot of people who buy painter would love to be able to produce portraits and paintings of their favorite photographs. This book only has one tutorial on portraits and it is oil based. It also spent a lot of time on effects for type, animation and web based graphics. Doesn't Adobe and Macromedia already have these areas well covered. I bought Painter because I want to paint.

I won't add much more to the previous reviews except to say "me too". The manual that comes with the program is very terse and often doesn't go into much detail on how to achieve a particular effect. The Wow! Book, on the other hand, is carefully organized to explore the software section by section, with LOTS of illustrations to us instruction-challenged people. You can use this book instead of the manual, IMO. And Painter is a superb program, it's nice to see it has a superb 3rd party book to support it.

I am the author's wife so, of course, I am biased.

The main thing I love is that Fractalia is interactive. There is a blog where readers can share their answers to the puzzles found in the book. It can be found at:

http://fractaliathebook.blogspot.com/

Each puzzle has many, many answers. The book gives only a few. There is no limit to the number of possible answers. It's fun to read what other people come up with, especially kids, so submit yours!

How can a puzzle have so many answers? My husband has specially designed this new brand of puzzles (which he calls "outties") that open out to an unlimited number of answers.

Read the book, have fun, and share your answers! That's what Fractalia is all about.

This is a great story. I really felt like I was inside the world the author created, and it was a place I wanted to be. You can tell that A.J. is in love with puzzles and fractals, and with his accessable writing style, he's able to share this love with a young audience. From an adult's perspective, I also really like how middle-school misfits become Fractalian heroes; It's the type of story that helps to build a child's sense of agency. If this book was around when I was a child, I think it would have been one of my favorites.

I think that Fractalia is fresh and original because it not only demonstrates the author's creativity, but encourages creativity in its readers. Rather than adding to the large library of titles teaching concrete skills such as mathematics through fiction, Fractalia promotes the more abstract skills of finding patterns, making analogies, and combining concepts. I've enjoyed it and am sure others will too.

This novel is unique, set in the most original "world" that I've read about in years. And the puzzles in the story are cool--they hooked me right into the story.

I really, really wish Fractalia would have been around when I was a kid. I would have loved it!

This book caught my attention for several reasons (other than my daughter left it for me to read) primarily the components of the title and the back cover.

- Fractalia, a place presumably based upon fractals.
- Episode 1. This is the first of a planned series. How long the series will be is not yet revealed.
- Reversing the Tipping Point. The Tipping Point by Malcolm Gladwell is one of my top 10 books. How does Fractalia relate to Gladwell's work? I needed to know.
- The back cover stated in part: "With degrees in philosophy and computer science, A.J. is currently working on his doctorate in cognitive psychology at the University of Massachusetts, Amherst. He is investigating the brainwaves of the 'aha' moment and how meaning is created out of apparent nonsense. A.J. lives with his wife Stephanie in Massachusetts. But really he lives on the border between sense and nonsense. Just ask his wife."

With a comment like that, I said to myself, this guy has to be writing some good stuff. After reading Episode 1, I can confirm that he is.

When reading fantasy or science fiction works, one problem is to bring the reader (us) into the new world within the book. The author needs to be careful to develop the place and develop the story without letting the new world (place) hinder the story. Authors of books with a well known setting, New York city in the early 1900's, or Shakespearean/Elizabethan England, for example, do not have to worry about this. They can get on with the story as we already know something of the place. In Fractalia, A.J. creates a new world and carefully brings us along.

Episode 1 covers the introduction to Fractalia, the Talian "people", introduces some "typical' modern day teenagers, and then brings them together. The cooperation between the Talians and the teenagers in meeting a challenge together results in success. Well yes, it is Episode 1, how could it be otherwise? Once you open the pages and begin to read a work of fiction, you put aside some things (at least for a while) and let the author take you on the way. If the author is successful, your willingness and his/her success will result in a good book experience. If the author is not successful, if the telling gets in the way of the story, you can become lost and the author looses you.

"The real unknown is between the known, they liked to say. Or, they would say, between two things there is always another."

A.J. has succeeded in sparking my desire for Episode 2.

Where is it? How long will I (we) have to wait?

"The wise know the difference between a puzzle and a mystery. A puzzle is for solving with the mind. A mystery is for enjoying with the heart."

You can pass the time waiting patiently for Episode 2 by practicing to solve some outties. You can find these outties on Fractaliatheblog.blogspot.com/

This is a great book. Only until you work with it will you find how good it is. My favorite thing in this book is what the author calls contraction mirroring and is discussed in chapters 4,5,6,8.

If you want to read this book, there are a couple of recommendations from me:

First, review your math: number systems, mods, logarithms, trigonometry, functions.
Second, prepare yourself for a book that is packed with information in each line. Don't expect even a line skip unnecessary.
Third, if you want to make a full use of book, don't read it and put it aside. You have to bear with the author and work out the examples. These two facts, combined with your willing to analyze the code algorithms will make you learn the fractals -relatively- deeply.

The bonus fact is that the authour explains how to create your own fractals in the last chapter.

As "the cons" I can say that the turbo basic programs are outdated. They need a good revision, possibly a port to C, Java (or maybe Ruby for the fans). In my opinion, a clean C code would do the trick.

Finally here is the chapter list:

i. Preface
ii. Acknowledgements
iii. Introduction

1. Counting and Number Systems
2. Numbers and Points
3. Meanders and Fractals
4. Spirals, Trees and Stars
5. The Analysis of a Fractal
6. Chance in Fractals
7. Poincare, Julia, Mandelbrot
8. Making Your Own Fractals

Appendix A. Complex Numbers
Appendix B. Programs
Bibliography
Index

In all my library of fractal books this one stands out as the most enlightening and the most useful. Hans Lauwerier is a master of Chaos and fractal theory. His method of analysis of IFS fractals is the best. He is just publishing a new book that should be rewarding as well.

This book is nicely written, well-organized and beautifully illustrated. It introduces most of the standard topics with a minimum of math, for example, iterated function systems, chaos, Mandelbrot and Julia sets, and random fractals. Among introductory semi-formal treatments of fractals I have seen, it strikes the best balance between concision, simplicity, and mathematical detail.

However, this somewhat dated volume needs a revision to upgrade the code from Basic to, say, Java. When the book was first published, microcomputers were relatively weak. Consequently, the book makes a few digressions into some rather involved algorithms designed to minimize memory use. Of course, today's machines are much more powerful. It is a lot simpler to use recursion (although this uses up memory liberally) in the fractal programs.

Finally, I think that the geometry could be made conceptually cleaner by mentioning that a general similitude (of which a contraction mapping is one example) on the plane can be written as a composition of rotations, translations, reflections, and scalings.

For more substantial treatments of fractals that don't demand too much math background, see "Fractals Everywhere" by M. Barnsley and "Introduction to Fractals and Chaos" by R. Crownover. However, one should read Lauwerier's slim and elegant volume before and after studying these more advanced works--before, as an introduction, and after, as a delightful summary and "bird's eye view" of the subject.

This is a nice book that will start you on the wonderful world of fractals. Contains BASIC source code for you to try. Very informative, you'll learn about the history of fractals and shows you the many different ideas and mathematical insights about fractals. This is really a good starter book (though you need background in algebra and trigonometry to follow the math equations).

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.

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.

This is a brilliant book. As an Architect, I was truly enlightened by the idea of the 'other' culture(s), having a valid scientific basis in fact. I was always told in Architectural school that the 'Africans',(including those in the diaspora) were a peoples without and writing systems, technological background and no culture. I'm glad to see evidence that this is not the truth. I thank the author for his contribution.

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 is a brilliant book. As an Architect, I was truly enlightened by the idea of the 'other' culture(s), having a valid scientific basis in fact. I was always told in Architectural school that the 'Africans',(including those in the diaspora) were a peoples without and writing systems, technological background and no culture. I'm glad to see evidence that this is not the truth. I thank the author for his contribution.

It was about the mid 1990's, still assimilating the big hype caused by the eventual and much-publicized proof by Andrew Wiles of Fermat's Last Theorem, when my curiosity (bolstered more by having seen a movie such as The Jurassic Park!) finally led me to taking a first college course on Chaos and Fractals at a California State school. At that time, the funny, surcastic, and somewhat sloppy foreign professor (who happened to be a country-mate of mine, for better or worse), had chosen the brand-new text "Fractals Everywhere" by Michael F. Barnsely for teaching our mid-size class consisting mainly of senior and first-year graduate students in math and sciences. I recall the discussion starting out by covering the basics about the metric spaces and sequences, and I having a head-start over many others coming fresh on the heels of a heavy-duty general topology course just in the previous semester (so for example I could show off to others on the first instruction day what it meant for two metrics to be equivalent). Still, I admit the semester went by without many of us really absorbing the nuts and bolts of the subject, for example why exactly topological transitivity was needed for chaos in an Iterated Function System, and why exactly some known fractals had the given fractional dimensions (eventhough we could compute them). However the students were generally happy to have scratched the surface of this vast, engaging subject, and for the time being it seemed about enough exposure for most of us. Consequently for me, during the several ensuing years in the late 90's the subject leapt mostly into the background, but nearly a decade later since I first took the college course, somehow it came back to the foreground in the company of several other applied subjects such as control, game theory, and information/coding theory.

Now looking back, I find Barnsley's text a very good choice having gone through at the time, but the title by Alligood, Sauer, and Yorke (as a recommendation by a college professor at a different school who had taught his students from it) seemed like a more well-balanced introduction to the area of dynamical systems. In fact I also recall at the time there was a discussion as to whether yet another text by Robert Devaney would have made for a better first course. The aforementioned professor duely noted that Devaney only dealt with the discrete dynamical systems, while A/S/Y treated both the discrete and continuous, hence making the choice of the latter a more suitable one. In any event, the rundown of the topics discussed in the 13 chapters of A/S/Y include: one and two dimensional maps, fixed points, iterations, sinks, sources, saddles, Lyapunov exponents, chaotic orbits, conjugacy, fractals and their dimension, chaotic attractors, measure, Lotka-Volterra models, Poincare-Bendixson theorem, Lorentz and Roessler attractors, stable manifolds and crises, homoclinic and heteroclinic points, bifurcations, and cascades. There are answers and solutions to the selected exercises, as well as extensive references at the back, making up an ideal setting for self-study. The level and style of exposition is targeted towards an advanced undergraduate student who is into applied math or engineering fields. Therefore the authors emphasize concepts and applications instead of getting bogged down in too much mathematical rigor or heavy use of the abstract machinery (which is of course needed for a thorough treatment of the subject at an advanced level; there are in fact several newer titles which all occupy this niche). Notationally and stylistically also, A/S/Y is very accessible and attractive. All in all, an excellent first excursion/introduction to one of the most fascinating areas of applied math, whether for classroom use, or for self-study.

[Review updated and reposted on 08/08/08]

When I purchased this book three years ago, I had only a rudimentary understanding of dynamical systems. Thankfully, all that was needed to get me started was some intermediate calculus and some basic college-level linear algebra. Since I had been doing both from the time I was a sophmore in high school, I had no trouble getting comfortable with it. The authors present dynamical systems in an easy-to-read style with tests that appear at the end of each chapter after you've had time to catch on.

If you're seriously thinking about getting started in dynamical systems, get this book!

This book presents brilliantly the foundations to Dynamical Systems and Chaos. You need to have some Linear Algebra, Calculus and Multivariable Calculus and Differential Equations knowledge. Full of exercises, computer experiments and Challenges. I think that the text looses some substance due to the lack of presenting more or all the solutions to the Exercises. They should be solved detailed in a Solutions Manual. Don't try to e-mail the authors for more solutions, they will not get them to you. This point is the only pitty in a text that is a great companion through chaotic dynamics. Also Very Brilliant for me at this Level are: Strogatz-Nonlinear Dynamics and Chaos, Kaplan-Understanding Nonlinear Dynamics, Gulick-Encounters with Chaos, Hilborn-Chaos and Nonlinear Dynamics, Devaney-An Introduction to Chaotic Dynamical Systems and A First Course to Chaotic Dynamics, Holmgren-A First Course in Discrete Dynamical Systems. More sofisticated maths but not too far away are: Schuster-Deterministic Chaos(graduate) and Ott-Chaos in Dynamical Systems (graduate).

I was enrolled in a course at GMU in which the draft version of this text was used. The math was not as difficult as some of the graduate texts, therefore it serves as a good intoduction for someone with as little as 2 years of undergraduate math. The challenges at the end of each chapter are more difficult than the regular problems, but they are meant to be. Many of the systems can be modeled on a spreadsheet. If you have any interest in Chaos, this book will only strengthen it.

This book is a must-own for anyone interested in nonlinear dynamics and chaos -- I also highly recommend the "Nonlinear Dynamics and Chaos" text by Strogatz.

I especially like the numerous diagrams that clarify everything so well in this book. In addition, the writing includes just the right amount of informal discussion to truly explain the material without retreating into jargon.

A favorite moment in the book is a "challenge" exercise that explains the famous "Period Three Implies Chaos" result: the reader is gently guided through 10 steps resulting in a proof of Sharkovskii's Theorem, a more general result that includes the Period 3 thing as a special case.

Buy it! Simply phenomenal.

Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! 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. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.

I appreciate Falconer's books on fractal geometry because they show the topic as it really is: a whole mathematical discipline on its own right and not just a nice temporary fashion.

It begins introducing basic topological concepts and then proceeds to develop the theory for several possible definitions of fractal dimension, showing the relations between them. Then it explores deeply the local geometry of different kinds of fractal objects, and studies some other geometrical situations, like the pojection of fractals (ever thought of a DIGITAL sundial? Here it is described!).

The book also includes a lot of applications to other areas of mathematics and physics, a great amount of graphics, and much more.

The text is suitable from third year undergraduate school and on. It is a larger but lighter version of "The Geometry of Fractal Sets".

I agree with all that was said by the other reviews here but add one important point. The physical layout, (typeface, drawings, whitespace etc.) of this book is brilliantly done. This is often overlooked by the producers of technical works who do it "on the cheap", but it is vital if one is to use the book day after day, as I have had to.

While the subject matter is not easy, this is an excellent book to motivate one to get stuck into the underlying mathematics. The reward is a little insight into the often beatiful theorems and practical results found in this stimulating field of study.

The first part of the book is essentially of a theoretical nature, with a thorough treatment of fractal geometry at a mathematical point of view. The second part on the other hand provides a flavour of the problems of fractal geometry in practice...so mathematicians as well as people interested in applications only should both find this book interesting. The maths are not easy but quite "understandable" for science undergrads...some notions of calculus or topology would help... but the introduction is excellent and allows anyone to follow the course of the book (but for understanding the proofs a good math background is required).

Excellent for understanding the geometrical properties of fractals.

The book opens the doors of mathematics: it isn't an easy door, but well worth the effort. It bridges the gap between beginner texts and advanced study and covers the basic material in a hard hitting manner. Those looking for "giltz" should look elsewhere. It is a book of great understanding and depth. Your unique Associates ID is: thefractaltransl.

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.

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.

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 I generate a fractal image with my PC?", from brownian motion to Julia sets. A must for reader interested in fractals (a bit out-of-fashion but still very interesting field).

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 be acheived.

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

The mathematician Felix Klein (1849-1925) made some great discoveries that can now be well understood by using computer graphics. Felix Klein is known for his work in non-euclidean geometry and for his work on the connections between geometry and group theory.

Some fairly simple mathematical ideas and algorithms reveal an endless universe of fractals. The book includes step-by-step instructions for writing computer programs allowing readers to perform further explorations.

[this review shall replace the already existing one]

Indras pearls provides a very well-made introduction to the basics of the theory of discrete groups acting on the complex plane. The whole discussion on the related limit sets had been accomplished in such a hand-by-hand method.
The reader starts from complex numbers and after he is led into the deepest concepts: Möbius trasformations, limit sets of discrete groups (Schottky, Fuchsian, ...).
These limit sets are related to another interesting topic in today maths: complex dynamics on the Riemann sphere (Julia sets, ...).
As known, computer experiments had been fundamental for supporting complex dynamics and the successive success of this latter topic helped to promote and increase the interests for discrete groups too: in fact this book evinces already strong interest in the visualization and in the study of the properties of such limit sets since '80s, due to the efforts of the same authors.
One of the major points of attraction in Indra pearls is that all the theory had been helped by displaying a lot of detailed and colorful pictures which, aside the historical biography of the mathematicians that contributed to this theory, set this book as one of the masterpieces in this topic, for his lucid
and fresh approach to basic concepts.
In addition, the presence of amusing comic-strips, explaining some topological concepts on manifolds (for example), guarantees the easy-learning for the reader and also the approach, as imaginaed and completely accomplished by the authors. In this direction, it is clear how passion had been squandered by authors.
The goal has been reached: finding an easy way to introduce the harsch theory of discrete groups.
Interested readers will be rewarded and also excited.
No doubts: this book strikes and it will be a corner-stone for present and future.

Indras pearls provides a very well-made introduction to the basics of the theory of discontinuous groups acting on the complex plane. The whole discussion about limit sets had been accomplished in such a hand-by-hand method.
That is, the reader starts from complex numbers and, after, he is taken into deepest concepts as Möbius trasformations and so to discontinuous groups (Schottky, Fuchsian, ...).
Limit sets of kleinian groups are related to another interesting topic in today maths: complex dynamics on the Riemann sphere (Julia sets, ...). The success of this latter topic helped to increase the interests for discontinuous groups too. Indra pearls also witnesses and resumes the last twenty years of efforts spent for studying the properties of the limit sets.
One of the major points of attraction in Indra pearls is that all the theory had been helped by displaying a lot of detailed and colorful pictures which, aside the historical biography of the mathematicians that contributed to this theory, set this book as one of the masterpieces in this topic, for his lucid
and fresh approach to basic concepts.
In addition, the presence of amusing comic-strips, explaining some topological concepts on manifolds, guarantees the easy-learning of the approach, achieved by the authors. In this direction, it could be evinced that authors were really enjoyed while writing.
The goal has been reached: finding an easy way to introduce the harsch theory of discontinuous groups.
Interested readers will be rewarded about their choice and also excited.

As a long-time reviewer of mathematics books, there was a time when I grew very bored with books written for the general mathematical audience. For years, it seemed mandatory that all contain a section on basic fractals and the Mandelbrot and Julia sets. It was not that the topics were not interesting, I found them fascinating, it was just that the explanations were all so similar that it became tedious to read them. Therefore, when I looked at the coverage of this book, I felt a pang of negative nostalgia, thinking that what I would find would be a repeat of what I had read so many times.
Well, I am happy to report that my pang was unfounded. The first chapter covers the language of symmetry, and some of the enormous number of forms in which it appears, which sets the stage for the fractal operations. A large part of the book is devoted to the patterns that are simultaneously symmetrical under two Mobius maps, which makes the analysis of fractals in this book different from what I have seen in others. Indra's necklace is a limit set formed by a chain of tangent circles, and is quite beautiful.
Very high quality figures are heavily used throughout the book to demonstrate the results of the operations. They are also beautiful, and in my opinion, some are works of art. Other mathematical operations that are used in the generation of the results are: matrix operations, group theory, non-Euclidean geometry, continued fractions, formal language theory, tiling of surfaces and function theory. The incorporation of so many different areas of mathematics really spices up the book, and makes it more enjoyable for a wider audience of mathematicians. It cannot be said that it is written for a general audience, the level of mathematics is beyond the non-mathematician, and one probably has to have the skill set of a junior or senior undergraduate math major in order to understand the explanations.
Mathematical results are very beautiful in their internal consistency and the power of the ideas. In this book, you also see some of the physical beauty that can be created by applying mathematics in the appropriate way