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What is the best book to learn about fractals? I am a total beginner, so the book should really start with basics and then introduce me to complex math, gradually.

Any suggestions?

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closed as off topic by Scott Morrison Oct 31 '09 at 18:35

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Why are you interested in learning about fractals? Actually, I don't have any idea why fractals might be interesting, other than "they look cool". –  Kevin H. Lin Oct 31 '09 at 17:55
Isn't that the entire point of math, finding stuff that looks cool and trying to understand it? –  Aaron Mazel-Gee Oct 31 '09 at 18:39
One of my favorite books on fractals is Indra's Pearls by Mumford et al. If I recall correctly, it begins at a pretty basic level, but I don't remember exactly how basic. It deals with a very special and simple, yet interesting and beautiful case of holomorphic dynamics. –  Darsh Ranjan Nov 10 '09 at 2:41

2 Answers 2

Falconer "The Geometry of Fractal Sets" is a very nice and readable beginning book. As to why one should bother study fractals (Kevin's comment): is the fact they look attractive not enough? If not, then remember that the sets of non-integral dimension do occur in other branches of mathematics. Some physical systems exhibit strange attractors. Mathematical fields like holomorphic dynamics are rich, and beautiful, and like all other parts of mathematics is often studied for richness alone, nevermind the applications. What other reason one needs?

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I did not mean to suggest that I think there's nothing interesting about fractals, nor did I mean to suggest that "they look cool" is not enough. I guess I should have phrased it differently. I was just wondering about examples of their mathematical interesting-ness, which you have now graciously provided :) –  Kevin H. Lin Oct 31 '09 at 18:55
Which bring us to the question why the question was labeled as "off topic" –  Boris Bukh Oct 31 '09 at 23:55

This page might help you. It has many links to books about fractals and by buying books on Amazon.com using those links you'll be also supporting the person that posted the links on the website.

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@Spinorbundle: I edited your question to make more clear the contents of the link you posted. Sorry that this was a complete change of your post --- let us know if you don't like it. More at tea.mathoverflow.net/discussion/35/commercial-links/#Item_8 –  Ilya Nikokoshev Nov 9 '09 at 19:36
@ Ilya: Thanks for editing my post. I'm sorry for the confusion, I didn't recognize that this site contains links to Amazon with the referral code of the site owner. Obviously I'm not the site owner, I just thought the comments on the book will be useful for the person who asked the question. So sorry again. PS: perhaps you can copy this comment to the meta.mathoverflow site since I'm not yet registered. –  Spinorbundle Nov 9 '09 at 20:10

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