Customer Reviews

Fractals: Endlessly Repeated Geometrical Figures (Princeton Science Library)

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4 star:		(2)
3 star:		(0)
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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 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.

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.

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

Timeless code and timeless explainations of the fractal processes of nature. One of the masters of the modern fractal world: I wish I had had this book when I started out! Your unique Associates ID is: thefractaltransl

Which it had more text to give it more of a lecture feel. I know quite a lot about the subject already and I just got it to see how someone else approached teaching the topic. Probably one of the best out there for a person just getting into the field. There are plenty of other texts that elaborate in greater detail about certain points but this is good enough of a start/foundation.

This book is an excellent resource for anyone wanting to explore fractals. It covers many different kinds of fractals and chaotic systems. It includes sample BASIC programs of many of the fractal equations. Although the BASIC programs are useful they are somewhat antiquated. I highly recommend this book.

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.