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The Beauty of Fractals: Images of Complex Dynamical Systems

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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 go
paraphrasing 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 and intuitive modes of thought co-exist, not at opposite poles,but complementing one another.

Intuition and analysis complement, rather than confound (or they should, gods-willing).

The artist and the scientist complement each other, i.e. Art and Science are not the opposing polarites of disciplines as some would have us think.

The thinker and the dreamer ARE one.

And this book has shown that the essence of beauty lies in the marriage of Art and Science.

(Disclaimer: Mere thoughts from a layman.)

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.

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.

Beauty, yes. Elegance, yes. The book is gorgeous, and the price is spectacular. Who says math is dull? Not when it's presented like this.

Fascinating photos, although the instructional text is indeed "complex" as the book itself states.

Anna Marie Fritz, author of "Funny Feline Fotos" and other amazon books.

One of the first books on fractals that gave info on the mathematics to creating them and what parameters or sections of the set that yield some beautiful renderings. The math is for a math major but still interesting.

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.

Amazon dot com gives no credit for my earlier reviews.... I wrote the first review without thinking or spell checking, fast. There are still parts of this book I can't duplicate! And parts that are just written so bad no one can understand them, but most of it stands the test of time, like Mandelbrot's article. This will probably be a classic in the future! I think the free Fractint documentation is probably better for a beginner or Hans Lauwerier's " Fractals".