Books about Chaos and Fractals

| 4 mins | Bob
tags: book, mathematics, science, studying

In the past few weeks, I unfortunately didn’t find much time to write more for my blog. So today, I have a simple list of awesome books I have in my shelf and found particularly helpful on my journey through chaos theory. If you are on a similar trip, they will definitely teach you a bit more than the typical Wikipedia article.

I have categorised them roughly:

  1. Popular-Science
  2. Computer-Science
  3. Academic Literature
  4. Picture Books

If you find any book missing in this list, please share it in the comments!

Chaos by J. Gleick (1987)

A very good historical summary of what it took to discover chaos, study chaos and explain chaos. In Chaos, James Gleick not only describes what happened back then, but lets you discover the simply mind-boggling science yourself.

Sync by S. Strogatz (2003)

Steven Strogatz is an exceptionally good lecturer at Cornell University as well as a very good writer that explains strange and complex concepts to you like not many other people can do. This book goes a step beyond “simple” chaos and shows you how nature manages to synchronise its elemental randomness back into order.

Computer-Science oriented Books

CPCB by C. Pickover (1990)

Computers, Pattern, Chaos and Beauty is my favourite of these books. It inspired me to write my own little programs to compute fractal images and attractors renders, which you can also find on my website. Cliff Pickover covers a lot of rather untypical topics and tells more about their mathematical background, but also provides some useful pseudocode algorithms.

The Science of Fractal Images by Peitgen et al. (1988)

Detailed and highly in-depth descriptions of fractal rendering methods and algorithms. Eight specialized researchers bring together their knowledge about all important aspects of the simulation and modelling of fractal growth, generation of random as well as deterministic fractals and patterns and show how to create digital representations of nature based on the science of fractals. Many pseudocodes are included.

Strange Attractors by J.C. Sprott (1993)

This could also be included in the Picture Books section, because this book contains a large collection of renders of two- and more-dimensional strange attractors. But in addition to that, each model is explained in great detail and BASIC program codes are provided you can run on your own PC. Although, this book and its programs are old, one can learn a lot of computer-science and mathematics from them.

Academic Literature

Introduction to Dynamical Systems by Brin and Stuck (2002)

Relatively little focus on chaos theory itself, but a great support for understanding how a system becomes dynamic and what types of systems there are scattered across different fields of mathematics. This basic knowledge helps to understand more advanced theories discussed in more specialised books.

Chaos and Fractals by Peitgen, Saupe and Jürgens (1992)

In my opinion, the standard work in this field. With this, you get over 800 pages of condensed knowledge about basically every aspect of chaos theory. The beauty you’ll find in this book is not necessarily in visually appealing images, but in the mathematics of this enthralling science.

Picture Books

The Fractal Geometry of Nature by B. Mandelbrot (1977)

Possibly the greatest and single most important publication about fractal images and what this field in mathematics is about. Benoît Mandelbrot himself shows every aspect of fractals he knew at the time and draws a connection between them. Depending on the edition, this book might cost you a fortune.

The Beauty of Fractals by Peitgen and Richter (1986)

Actually beautiful and high-quality pictures of fractals and chaotic objects in a large-format book with great explanations of what is depicted and some theory behind it.

The M\(\alpha\)TH \(\beta\)OOK by C. Pickover (2009)

A great timeline of important discoveries in mathematics. From 150 Million B.C. to 2007, Cliff Pickover shows 250 milestones with a great image and provides a short summary of what it is about and why it was important. The hardback edition is particularly nice to flip through.