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Fractals Everywhere

Michael F. Barnsley
Dover Publications
Publication Date: 
Number of Pages: 
Paperback with CDROM
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Luiz Henrique de Figueiredo
, on

This is a reissue of the second edition of Barnsley's book, originally published in 1993. It is the main account for the iterated function systems approach to fractals introduced by the author. This book is a classic now.

The current book calls itself a new edition because it includes 16 pages of new color plates, a new foreword, and a CD with IFS software. The text itself remains exactly the same as in the second edition. The typos remain and unfortunately there is no errata in the book and I could not find one in the web site mentioned in the foreword.

The book remains an excellent example of accessible and interesting applied metric topology. The mathematics is alive and rigorous without being pompous. It is complemented by not-to-be-missed hands-on computer-aided experimentation.

Naturally, the computer equipment mentioned in the book is ancient history now and unfortunately the BASIC programs are not immediately useful because computers no longer come with BASIC by default. Nevertheless, the code is simple and clear and is easily adapted to current computing environments, though probably not many readers will have that inclination. Everyone will certainly enjoy playing with the software in the CD, which runs in current machines (Windows only, unfortunately).

More importantly, the pictures — which play a central role in the book — are not of the quality expected now. This gives the book a dated appearance. But do not let this hamper your enjoyment of the mathematics in this still exciting classic.

Luiz Henrique de Figueiredo is a researcher at IMPA in Rio de Janeiro, Brazil. His main interests are numerical methods in computer graphics, but he remains an algebraist at heart. He is also one of the designers of the Lua language.

Introduction to the Dover Edition
I Introduction
II Metric Spaces; Equivalent Spaces; Classification of Subsets; and the Space of Fractals
III Transformations on Metric Spaces; Contraction Mappings; and the Construction of Fractals
IV Chaotic Dynamics on Fractals
V Fractal Dimension
VI Fractal Interpolation
VII Julia Sets
VIII Parameter Spaces and Mandelbrot Sets
IX Measures on Fractals
X Recurrent Iterated Function Systems
Selected Answers
Credits for Figures and Color Plates