The Beauty of Fractals: Images of Complex Dynamical Systems

by Peitgen

The authors present an unusual attempt to publicize the field of Complex Dynamics, an exciting mathematical discipline of respectable tradition that recently sprang into new life under the impact of modern computer graphics. Where previous generations of scientists had to develop their own inner eye to perceive the abstract aesthetics of their work, the astonding pictures assembled here invite the reader to share in a new mathematical experience, to revel in the charm of fractal frontiers. 184 illustrations in 211 parts, 88 in color.

Genres: Mathematics, Nonfiction, Science, Reference, Art

199 pages, Hardcover

First published July 1, 1986

Reviews

[Matt · Rating 4 out of 5]

Back in 1987 – before the Internet – this book was an eye- (and mouth-) opener. PCs weren't hardly able to reproduce images like the ones presented in this book.



Now the book has become kind of obsolete: The underlying math you can learn from Wikipedia and other sites. The graphics you can make yourself with one of the many free fractal generators (see above and below).



But chaos can still look cool, doesn't it?




This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

[Rodd Halstead · Rating 5 out of 5]

The first major book with pictures of Mandelbrot Set zooming. Articles range from do it yourself (algorithms and coordinates to make Mandelbrot and Julia set images), to meditations on the larger meaning and import of fractals and chaos.

[Olivia Demeter · Rating 5 out of 5]

One of my favorite books of all time. And one of the few I can say has dramatically changed my perspective on life. I come back to it time and time again whenever I need to be reminded of the beauty and complexity of the universe.

[Kalle Wescott · Rating 5 out of 5]

I re-read /The Beauty of Fractals: Images of Complex Dynamical Systems/, by Heinz-Otto Peitgen:

https://link.springer.com/book/10.100...

Long ago, this book and Mandelbrot's work were among the inspirations leading me to decide to go back to school in computer science to pursue further study in computer graphics and animation.

It's a classic.

[Brok3n · Rating 5 out of 5]

Chaos mathematics coffee table book

I first became aware of chaos mathematics in 1976, when Robert M. May published his famous Nature review "Simple mathematical models with very complicated dynamics", a preliminary exploration of what we now call the Logistic Map. Chaos research proceeded apace through the late 1970s and early 1980s, to the point where some of the questions May had raised were answered. It also became evident about then that there were connections between chaos mathematics and fractals, which had been explored earlier by Benoît B. Mandelbrot, who published The Fractal Geometry of Nature in 1977. In particular, there are deep connections between the logistic map explored by May and a particular fractal discovered by Mandelbrot that became known as the Mandelbrot Set.

Now, in 2024, many people have heard of the Mandelbrot Set and almost everyone has seen pictures of it. Before 1984 such pictures barely existed. Heinz-Otto Peitgen and Peter H. Richter, respectively professors of Mathematics and Physics at the University of Bremen, set about to produce color graphic representations of the Mandelbrot Set and other fractals. They had access to what at the time passed for powerful computers. Some of their pictures appeared at an exhibition entitled "Frontiers of Chaos". This book is a collection of pictures from the exhibition. In addition, the text of the book explains much of the math behind the pictures.

There are few things more subjective than beauty, so it will be understood that I express only a personal opinion when I say that the pictures are stunningly beautiful. I had seen images of the Mandelbrot Set and other fractals before I received this book as a gift, but none that I had seen were like this. The cover image, in particular, was one of the most beautiful pictures I had ever seen, and I still hold it so almost thirty years later.

In the thirty years since Peitgen and Richter produced these pictures powerful computers have become far more widely available. I include here a fractal image I produced on my desktop computer in 2015 as my answer to one of the questions in a problem set in Functional Analysis, a course I took as a first-year grad student in Applied Mathematics. This image reproduces Figure 42 of The Beauty of Fractals: Images of Complex Dynamical Systems, except that that image is in drab black and white, whereas mine, since I did the problem set over Halloween, I did in orange, black, and yellow. On my desktop it took mere seconds to produce this image.



Color images in The Beauty of Fractals are much prettier than this homegrown example.

Blog review.

[Amy Qualls · Rating 2 out of 5]

I didn't check this book out for reading purposes, but instead for pattern ideas, and I didn't see anything that grabbed me. Book itself is probably decent; I'm just not the right audience for it.