The Beauty of Fractals: Images of Complex Dynamical Systems

by Heinz-Otto Peitgen and Peter H. Richter

Book Overview

In 1953 I realized that the straight line leads to the downfall of mankind. But the straight line has become an absolute tyranny. The straight line is something cowardly drawn with a rule, without thought or feeling; it is the line which does not exist in nature. And that line is the rotten foundation of our doomed civilization. Even if there are places where it is recognized that this line is rapidly leading to perdition, its course continues to...

• Format: Hardcover
• Language: English
• ISBN: 3540158510
• ISBN13: 9783540158516
• Release Date: July 1986
• Publisher: Springer
• Length: 202 Pages
• Weight: 2.40 lbs.
• Dimensions: 0.8" x 8.4" x 11.0"

Customer Reviews

The Essence of Beauty

I spent all last evening reading snippets of The Beauty of Fractals (those few paragraphs that a layman could understand) and admiring the sheer beauty of the diagrams/maps. I had not realised there was an aesthetic component to mathematics, and I certainly did not know that aspects of what is generally thought of as a dry science can be so visually appealing, not to say stunning.I cannot understand why some people would argue the intrinsic artistic merit of something computer-generated and 'unnatural', when the results speak for themselves.Beauty, true, is perceived, and lies in the eye of the beholder. It can be very subjective. But there are certain aspects of visual appeal that go beyond that. One would think that a symmetry of form, the complementary use of colours, the balance of shape and form, light and shade, arcs and curves--all these combine to give an objective, irrefutable fact of beauty that transcends thought and emotions, if not the senses.In a couple of the chapters, it was said, and here I paraphrase:The two modes of analysis and intuition as human means of understanding the natual world--need they be considered at opposite poles? Do they not complement one another? Are the thinker and the dreamer not one?I find that very intriguing, just as I find the idea of chaos and order existing together in natural, dynamic processes being actually TYPICAL of Nature.The word 'Chaos' has such negative connotations, implying confusion and destruction, but if I were to replace it with the word 'Disorder', then things begin to fall into place.There can be no Order if there were no Disorder, for how then would we know the difference? In fact, one of the writers go so far as to say that it is the very existence of Disorder within Order that confers the essence of beauty found in Nature.That is so true. It is the very non-linear aspect of Nature, that which mathematics, up till Mandelbrot, have been unable to map, that is so appealing in the visual sense.In Nature, which, apart from abhorring vacuums, also has no place for a straight line (oh, how the poor, innocent straight line is maligned in the preface), beauty is inarguable, irrefutable, and only after that does it have history and context, different to and for each beholder.So both Chaos/Disorder and Order co-exist in Nature, hand in hand. Order alone, rigidly disciplined, artificially-imposed, seems to require Disorder to breathe life into it.Taking this a step further, our perception of beauty in all things is affected by Nature.In yet another chapter, someone quoted someone else and here I goparaphrasing again.Beauty in science is the same as beauty in other disciplines-art, music,literature, what have you. 'A fog of events, and suddenly you see a connection. It expresses a complex of human concerns that goes deeply to you, that connects things that were always in you that were never put together before.'The thinker and the dreamer co-exist within each person, just as the analytical an

Swirly

Although one of the earliest titles to bring fractals into the mainstream, 'The Beauty of Fractals' isn't as visually exciting as the follow-up, 'Chaos and Fractals', and it's a very dry read - in 1986 complex dynamics were an esoteric field of mathematics that had yet to transfer to student posters and rave videos. At this price it's restricted to people who absolutely need it, although along with 'Godel, Escher, Bach' it's one of the seminal hackish coffee-table books.

One of the more important textbook in the subject

A very good work, with wide subjects and deep analysis, not for beginner but you are not required to be a specialist to read it. Even if it shows the structure of lecture notes, it maintains a strong cohesion, embracing in a single context different fields, such as computer graphics and statistical physics.

Pretty Pictures,Hard text and No Code!

The picture give the wrong impression: this is not a beginner's book. Some of the text is impossible even for experts to understand. There are cvery good articles and necessary data in this book, but for the starting programmer it is just high tone language of professors and frustration. Pictures and references are not everything. Your unique Associates ID is: thefractaltransl.