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Benoit Mandelbrot
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The Fractal Geometry of Nature Hardcover – January 1, 1982

by Benoit B. Mandelbrot (Author)
4.6 4.6 out of 5 stars 146 ratings
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Clouds are not spheres, mountains are not cones, and lightening does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.

Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

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  1. Print length
    468 pages
  2. Language
    English
  3. Publisher
    Times Books
  4. Publication date
    January 1, 1982
  5. Dimensions
    8.28 x 1.41 x 9.33 inches
  6. ISBN-10
    0716711869
  7. ISBN-13
    978-0716711865
  8. See all details
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The Amazon Book Review
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Editorial Reviews

Amazon.com Review

Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.

The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds.

Review

“A rarity: a picture book of sophisticated contemporary research ideas in mathematics.” ―Douglas Hofstadter, author of Godel, Escher, Bach

Product details

  • Publisher ‏ : ‎ Times Books; 2nd prt. edition (January 1, 1982)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 468 pages
  • ISBN-10 ‏ : ‎ 0716711869
  • ISBN-13 ‏ : ‎ 978-0716711865
  • Item Weight ‏ : ‎ 2.48 pounds
  • Dimensions ‏ : ‎ 8.28 x 1.41 x 9.33 inches
  • Customer Reviews:
    4.6 4.6 out of 5 stars 146 ratings

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Benoit Mandelbrot

Benoit Mandelbrot

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Customer reviews

4.6 out of 5 stars
4.6 out of 5
We don’t use a simple average to calculate the overall star rating and percentage breakdown by star. Our system gives more weight to certain factors—including how recent the review is and if the reviewer bought it on Amazon. Learn more
146 global ratings
Natural anomalies within our aberrant universe
5 Stars
Natural anomalies within our aberrant universe
We are in 1982, Mandelbrot got a computer and is showing us the geometry nature has been using. Have a good look through that window. Euclid’s geometry works for human made stuff (before 3D printers) but fails with clouds, trees, your hair (in that reflection) and so on. Nature is ingenious using a blend of chance, scale and repetition creating regular irregularities here called fractals. Being a maverik, Mandelbrot introduced the fractal dimension assuming that "to see is to believe". Lucky us. There are plenty of puzzling plots in this book. Some even defined as nondifferentiable monsters, say a snowflake (Koch’s monster). What a show! But Madelbrot’s erudition and eccentricity makes this book a fractal itself. Often diverging and sharing bits of history and biographical notes. But always discussing typical anomalies within our aberrant universe.
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Top reviews from the United States

John D. Goulden
5.0 out of 5 stars A must have for math nerds
Reviewed in the United States on August 3, 2023
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This was a replacement, my old copy was water-damaged in storage. Every math nerd should have this book; it is interesting, well-written, and has lots of great illustrations.
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E. Dryere
5.0 out of 5 stars A great insight into the world of fractals
Reviewed in the United States on February 17, 2010
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This is a great book for someone looking to discover what all the hullabaloo is about fractals. It provides a wonderful insight into the mind of one of the great mathematical geniuses of our time, Benoit Mandelbrot. I think some people will find his writing style a bit too stodgy, almost arithmetical, but I find it interesting. I especially appreciate how marks off when he's going to be tangential with special brackets. Mandelbrot doesn't delve into too many rigorous mathematical proofs of the various topics he discusses. He broaches each subject in such a way that should be accessible to people from a wide array of sciences and disciplines. I don't recommend this book if you're trying to figure out how to create simple fractal programs. But I enthusiastically recommend it if you want to learn more about fractals, discover a new way to think about and understand nature, or are simply looking for a good bit of erudition.
6 people found this helpful
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Wquilliam
5.0 out of 5 stars Who couldn't love Mandelbrot
Reviewed in the United States on April 10, 2014
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Mandelbrot... R.I.P. my friend... he was an angel sent from infinity to infinity and beyond... although he is gone from the known human world, Mandelbrot is a fractal of the universe and forever spiraling deeper, yet closer, yet wait.. no.. farther.. no.. ah who knows. Fractals are mystery! Oh but hold on... I have this great book written by Mandelbrot on the Fractal Geometry of Nature! That'll tell me what i need to know about where Mandelbrot went in the afterlife. But come on, ok I'll get serious here, this book will get you into some trouble. This is no light darling sweetheart. This is not a book to the easy side of the galaxy of things. It's a full blown mathematical textbook of equations, expecting the average joe to be the all-in-one scientist abroad, just back from holiday and ready for the thick of it all. He dials in to his secretary to say, "Miriam--I want no phone calls today, you understand?? Under no circumstances shall I be answering any calls.. and NO interruptions... You got it!? NONE! WHATSOEVER!" ..and he slams the phone back in the cradle, blood pressure quickly rising, pops some stress-relievers, takes a seat at his work desk, and opens the book... The Fractal Geometry of Nature. Three weeks later his secretary finally gets the door open to his office by prying at the lock with her hairpin. She gasps! Turns her head and weeps.. the man had keeled over from dehydration and malnutrition, face down in The Fractal Geometry of Nature.
5 people found this helpful
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Daniel Barham
5.0 out of 5 stars A treatise on fractals as a unifying phenomenon
Reviewed in the United States on April 11, 2015
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The magnum opus of a true genius. Within this book lies the legacy of a profound academic and perhaps the most rigorous and complete analysis of fractal geometries that has ever been created. It is a balanced look at fractal geometries that fills a niche for all levels of expertise. As a mathematical novice you can enjoy the pictures and narrative and as a master there is a trove of insight. If you are interested in how fractals are rife throughout nature and how these various geometries can be explained using Benoit's mathematics, this is the book for you.
12 people found this helpful
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Jane Weird
4.0 out of 5 stars A great read for most
Reviewed in the United States on November 22, 2011
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Of course I love this book; I read it for the first time when I was just a young teen; now upon re-reading it, I realize how difficult so much of the mathematical material is. Of course, Mandelbrot wrote it and labeled it as an 'essay', thus intended for a wide variety of disciplines and backgrounds in order to reach a maximum audience, but his coining it as targeted for a 'broad' audience may have been referring to 'peers in similar fields' because despite all the math I took in college, much of the digressions in this book are lost on me. Still, so much of the content is accessible immediately through the written content and the visuals are unmistakably striking, especially for such old computer graphic technology. I would recommend this for anyone interested in the studies of fractal geometry, chaos theory, and turbulent dynamics.
12 people found this helpful
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Elijah Cook
5.0 out of 5 stars Good Stuff!
Reviewed in the United States on July 10, 2018
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Very interesting and educational from the father of fractals himself! This is a must if looking into the math of fractals.
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Kenneth R. Bolser
5.0 out of 5 stars The book that popularized fractal geometry.
Reviewed in the United States on February 5, 2013
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For the general public, this book helped set in motion the concepts of, and the potential to understand natures' geometry. this book also gives the ground work for the potential fin art and illustration more reflective of the geometry of nature - and a new tool for the arts. The graphics are still inspiring. A must for anyone intetrested in the Mandelbrot set, fractal geometry and the forms that evolve from chaotic dynamics.
4 people found this helpful
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pythonguy
5.0 out of 5 stars This book will blow your mind
Reviewed in the United States on August 28, 2012
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Like Douglas Hofstadter's "Godel, Escher, Bach" this book is an excellent mix of crazy awesome math and beautiful pictures. Much of the text is accessible to the math layperson, but the math itself is pretty crazy. Way beyond me, but I still pick it up and read it on many different evenings to meditate on the complexity of it all and the amazing pictures.
2 people found this helpful
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Top reviews from other countries

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Roberto Rigolin F Lopes
5.0 out of 5 stars Natural anomalies within our aberrant universe
Reviewed in Germany on August 13, 2018
Verified Purchase
We are in 1982, Mandelbrot got a computer and is showing us the geometry nature has been using. Have a good look through that window. Euclid’s geometry works for human made stuff (before 3D printers) but fails with clouds, trees, your hair (in that reflection) and so on. Nature is ingenious using a blend of chance, scale and repetition creating regular irregularities here called fractals. Being a maverik, Mandelbrot introduced the fractal dimension assuming that “to see is to believe”. Lucky us. There are plenty of puzzling plots in this book. Some even defined as nondifferentiable monsters, say a snowflake (Koch’s monster). What a show! But Madelbrot’s erudition and eccentricity makes this book a fractal itself. Often diverging and sharing bits of history and biographical notes. But always discussing typical anomalies within our aberrant universe.
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Roberto Rigolin F Lopes
5.0 out of 5 stars Natural anomalies within our aberrant universe
Reviewed in Germany on August 13, 2018
We are in 1982, Mandelbrot got a computer and is showing us the geometry nature has been using. Have a good look through that window. Euclid’s geometry works for human made stuff (before 3D printers) but fails with clouds, trees, your hair (in that reflection) and so on. Nature is ingenious using a blend of chance, scale and repetition creating regular irregularities here called fractals. Being a maverik, Mandelbrot introduced the fractal dimension assuming that “to see is to believe”. Lucky us. There are plenty of puzzling plots in this book. Some even defined as nondifferentiable monsters, say a snowflake (Koch’s monster). What a show! But Madelbrot’s erudition and eccentricity makes this book a fractal itself. Often diverging and sharing bits of history and biographical notes. But always discussing typical anomalies within our aberrant universe.
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One person found this helpful
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Berchiesi Gianfrancesco
5.0 out of 5 stars Da una idea brillante ad una matematica complessa
Reviewed in Italy on June 14, 2018
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L'idea di adattare la geometria classica alle forme più disparate è stata un'idea vincente. Da una idea semplice si è poi sviluppata una geometria che ha ovviamente le sue difficoltà e che necessita di una lettura e di una ri-lettura. Quello che più mi affascina è che questa teoria prevede il Caos.
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Adrian Murariu
5.0 out of 5 stars I love it so much I will read 1million times
Reviewed in the United Kingdom on December 30, 2017
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BUY IT, ITS AMAISING
If you are in any way considering doing anything with fractals, there's no reason to have other people's books and not this one .
This is one of the most important sources of understanding fractals, because it comes from the creator of the geometry itself .
I just got the book, It has a square aspect instead of a normal rectangular aspect.
I love it so much I will read 1million times.
There's cools drawings inside and all kinds of explanations , I'm so happy with this there's no words to describe .
Love to the author .
3 people found this helpful
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jeremy whitehorn
5.0 out of 5 stars Five Stars
Reviewed in Canada on May 18, 2015
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Just what I wanted...
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srl38
5.0 out of 5 stars Excellent ouvrage sur les fractales
Reviewed in France on February 25, 2013
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Ca faisait des années que je cherchais cet ouvrage et là je l'ai trouvais
Je le lis en ce moment
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