Fractals: Endlessly Repeated Geometrical Figures [Paperback]

Hans Lauwerier (Author), Sophia Gill-Hoffstadt (Translator)

Book Description

Publication Date: May 21, 1991

Fractals are shapes in which an identical motif repeats itself on an ever diminishing scale. A coastline, for instance, is a fractal, with each bay or headland having its own smaller bays and headlands--as is a tree with a trunk that separates into two smaller side branches, which in their turn separate into side branches that are smaller still. No longer mathematical curiosities, fractals are now a vital subject of mathematical study, practical application, and popular interest. For readers interested in graphic design, computers, and science and mathematics in general, Hans Lauwerier provides an accessible introduction to fractals that makes only modest use of mathematical techniques. Lauwerier calls this volume a "book to work with." Readers with access to microcomputers can design new figures, as well as re-create famous examples. They can start with the final chapter, try out one of the programs described there (preferably in a compiled version such as TURBO BASIC), and consult the earlier chapters for whatever is needed to understand the fractals produced in this way. The first chapter, which builds on the relationship of binary number systems to the "tree fractal" described above, is the best place to start if one has no computer. There will be much to enjoy on the way, including the beautiful color illustrations.

Editorial Reviews

Review

This is a valuable, attractive and unpretentious introduction to a fascinating subject. -- American Scientist

Language Notes

Text: English (translation)
Original Language: Dutch --This text refers to an out of print or unavailable edition of this title.

Product Details

• Paperback: 224 pages
• Publisher: Princeton University Press; 1st edition (May 21, 1991)
• Language: English
• ISBN-10: 0691024456
• ISBN-13: 978-0691024455
• Product Dimensions: 8.5 x 5.5 x 0.5 inches
• Shipping Weight: 10.7 ounces
• Average Customer Review: 4.8 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #1,233,301 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

5 of 5 people found the following review helpful:

4.0 out of 5 stars Very nice book...short but packed full of information, October 19, 1999

By A Customer

This review is from: Fractals: Endlessly Repeated Geometrical Figures (Paperback)

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).

4 of 4 people found the following review helpful:

5.0 out of 5 stars A Excellent Introduction to Fractals, June 20, 2001

By A Customer

This review is from: Fractals: Endlessly Repeated Geometrical Figures (Paperback)

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.

3 of 3 people found the following review helpful:

5.0 out of 5 stars A Classic of Fractals, July 29, 2001

By 

R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews
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This review is from: Fractals: Endlessly Repeated Geometrical Figures (Paperback)

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.