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Fractals: A Very Short Introduction

Kenneth Falconer
Oxford University Press
Publication Date: 
Number of Pages: 
Very Short Introductions
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Charles Ashbacher
, on

This book matches the title in terms of content and length. It is a complete introduction to the fundamentals of fractals and is written at a level where an advanced high school student can understand it. There are several images embedded in the text but they are all black and white so the pictures of the Mandelbrot and Julia sets lack the majestic nature of the colored ones.

The primary mathematics used to describe fractals are the complex numbers, logarithms, basic function notation and the concept of repeatedly iterating a function. Although the necessary use of a computer to plot the points of the sets is mentioned, there are no lines of computer code in the book.

If you are not familiar with the mathematical basis of fractals, the basic history of the development of the field and how they can used to describe many natural processes, then this book will serve as an effective primer. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

1. The fractal concept
2. Self-similarity
3. Fractal dimension
4. Julia sets and the Mandelbrot set
5. Random walks and Brownian motion
6. Fractals in the real world
7. A little history
Further reading