Fractals Everywhere

by Michael F. Barnsley

Introduces fractal geometry, and covers transformations on metric spaces, dynamics on fractals, the fractal dimension, fractal interpolation, Julia sets, parameter spaces, and measures on fractals

Genres: Mathematics, Science, Textbooks, Geometry, Computer Science, Biology, Nonfiction

560 pages, Hardcover

First published January 1, 1988

About the author

Michael Fielding Barnsley

Reviews

[Amar Pai · Rating 4 out of 5]

As math books go, this is pretty great. The illustrations really benefit from the author's sense of humor. The illustrations and diagrams frequently make use of smiley faces, words and other reassuringly non-abstract forms. I find it actually helps me learn cos it's less intimidating while still conveying the concepts. I guess it's easier to do this when you're dealing with 2d geometric objects, but in general hardly any math textbooks ever seem to show a sense of humor or any kind of personality.

Barnsley's book about fractals is based on the course which he taught for undergraduate and graduate students in the School of Mathematics, Georgia Institute of Technology, called Fractal Geometry. After publishing the book, a second course was developed, called "Fractal Measure Theory".[1] Barnsley's work has been a source of inspiration to graphic artists attempting to imitate nature with mathematical models.

Man I would've loved to have taken that class!! It's frustrating cos I know that without the context of a class and required homework and tests, I'll never get all the way through this book, yet I also know that I totally COULD understand this book if I put enough effort into it. This is unlike most math textbooks, which always get to a point where I give up knowing I'll never really understand the material. Here there aren't a lot of prereqs-- topology, analysis and linear algebra all are used heavily, but not in a super complicated way.

I guess I'm not the first person to get bitten by the fractal bug. Mandelbrot set is just so fascinating. (It's what got me started on things, although I confess to still not really getting the Julia set/Mandelbrot set connection, nor the 'reason' why the boundary of the set looks the way it does. Or even what such a reason would look like. Something to do with the periodicity of complex polynomials? multiplying by i? unit circle?)

Also fascinating: the concept of fractal dimension, and experimental observations of same. Did you know cauliflower has a fractal dimension?

[Hannah Thomas · Rating 3 out of 5]

This was an "iffy" for me. This book was difficult at times to read that I did have to go back and re-read things, mainly because this is very new material to me. I have never heard of fractals until I have read this and I did learn a bit. You can tell that this book was compiled, by the help of several other mathematicians, experienced in the branch of fractals. The only thing about fractals is that they are not studied as much as other subjects within the area of mathematics. Hence, they are rare and only about...maybe 100-ish individuals study this.

[HM · Rating 4 out of 5]

در دقایق طبیعت که باریک شویم می بینیم هیچ شکل هندسی منظمی مانند خط و دایره وجود ندارد و با اشکالی پیچیده و نا منظم مواجه هستیم. در اینجاست که هندسه نوین فراکتالی که بر اساس خاصیت خود تشابهی بنا شده راهگشاست در این کتاب ارزشمند مایکل بارنسلی با ارایه توپولوژی و مباحث دقیق ریاضی به کاربردهای شگفت انگیز تئوری فوق در فشرده سازی نصاویر و پیش بینی پدیده های آشوبناک مثل آب و هوا و بازار بورس اشاره می کند

[Marco Bitetto · Rating 5 out of 5]

This is a reasonably good introduction into how fractal mathematics can be used in everyday work.
The book is a bit challenging for the mathematically phobic. But, it is nevertheless readable and
understandable.

[Gary · Rating 5 out of 5]

A math textbook about fractals. My first intro to the Shadow Theorem.

[Robert · Rating 2 out of 5]

Sigh, good books on fractals are so rare. This is, unfortunately, typical.

[Joey Zhouyuan · Rating 4 out of 5]

Awesome illustrations. Combine ideas of dynamical systems (chaos) and computer graphing. Systematically organized as balance the mainstream of the modern math branch in such intro level reading.