You have heard of fractals. You may even have read about them in a popular magazine like BYTE or Scientific American, or in a popular science book like James Gleick’s Chaos: making a new science [1]. You want to know more, but the standard references are mathematically intimidating. Michael McGuire’s delightful new book is for you.

Many people will want to have this pleasant little volume around their offices or homes. While the text is primarily a lucid introduction to fractals, more than half of the pages are devoted to illustrations. Some of these pictures are standard computer-generated synthetic images, but the majority are photographs of fractal patterns in nature.

The photographs, all of which are in black and white, are wonderful. The subject matter ranges from flowers, ferns, and trees to waterfalls, mountains, and caves. Except for one classic Ansel Adams print, all the photos were taken by McGuire. The monochromatic presentation allows the viewer to concentrate on the geometric complexities of the shapes and textures of flora and terrain.

The design of the book is attractive. At first glance, it appears to be primarily a coffee-table book of photographs. Upon closer examination, it is revealed to be a lavishly illustrated monograph on that most visual branch of mathematics, fractal geometry.

McGuire’s book originated from a short essay that concentrated on how the emergence of popular interest in fractals has affected the approach of photographers to natural phenomena [2]. This volume is much broader in scope. The first dozen pages give the reader an intuitive feel for what a fractal is, using a combination of concise writing, photographs, and drawings. McGuire then launches into a surprisingly comprehensive overview of fractal research. The emphasis is always on clarity and intuition rather than mathematical rigor, and the approach succeeds wonderfully.

After the reader has completed the painless journey through this short book, he or she will know much about fractals. McGuire discusses geometric replacement rules, computing fractal dimensions, statistical versus absolute self-similarity, iterated function systems, fractal compression, and deterministic chaos. The popular Julia and Mandelbrot sets are described and illustrated.

The last section of the book is closest in tone to McGuire’s original essay. In it, he shows how painters and photographers have observed the complex patterns in nature for decades. He contends that this artistic attention led scientists to the study of fractals in the first place. The popularization of scientific results has in turn attracted more artists to fractal forms.

For those wishing to learn more, an annotated bibliography is provided. No index or table of contents is provided.

This book has several audiences. First, it will appeal to photography enthusiasts. Second, it is a good introduction to the fundamentals of fractal mathematics. No technical knowledge beyond high school mathematics is needed. McGuire should be proud of having produced such a good book.