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absalom's avatar

What kind of math course should I take if I want to learn about fractals?

Asked by absalom (7552 points ) November 8th, 2010

I am not the kind of person that one might say has a head for numbers, but I have lately found fractals to be intensely fascinating after discovering their presence in the structure of a novel.

I’m a college student. Here are the options:

—Elementary Functions and Analytic Geometry
—Math and Calculus Applications for Life and Social Sciences [doubtful]
—Introduction to Linear Algebra
—Discrete Mathematics [doubtful, but seems interesting]
—Elementary/ Differential Equations
—Abstract Algebra
—Complex Analysis [this seems to be maybe the most relevant]

I’d be auditing the course because there’s no way in hell I’d manage an A in math, but I’m really interested in fractal geometry.

So, which of these should I pursue? Your help is appreciated.

Also, if you have any book recommendations regarding fractal geometry, especially if it’s related to Wacław Sierpiński and/ or infinite recursion, I’ll take that, too.

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7 Answers

ETpro's avatar

The actual math required to build a fractal is quite straightforward. The thing that sets it apart from ordinary high school algebra is that instead of an equals sign in the equation there is a funny looking sign like a equals, but with a little barb sticking out, like half an arrowhead on one end of the upper straight bar and the other end of the lower straight bar. This means in math an iteration, in other words, the result of the first time through the equation to the right feeds back into the value on the left and the equation runs again with the new value, over and over. This gives the Mandelbrot Set and the Julia Set and others like them their endless regression to ever finer detail.

Benoit Mandelbrot himself wrote a book about how to teach Fractal Geometry in math classes. It’s for math teachers, but if you have a decent command of math you can probably grasp it. It’s called Fractals, Graphics, and Mathematics Education (Mathematical Association of America Notes)

Also, this site has a whole section on online learning resources for Fractal plus a lot of other cool math that applies to art. Enjoy. It is certainly a fascinating subject.

Finally, check out these two questions of mine. They have links to some truly wonderful videos on fractals.
1—How does the universe impose its fractal-like patterns of order on chaotic systems?
2—How small can the repetitive fractal features of nature get?
1—How does the universe impose its fractal-like patterns of order on chaotic systems?
2—How small can the repetitive fractal features of nature get?

Trillian's avatar

My brain just exploded. It’s beyond me, I’ll just sit and look at the fascinating images, but now I’ll drool at the same time. (Claps hands) Oooooo, pretty…..

ratboy's avatar

Check the prerequisites—math courses usually must be taken in a certain order.

Fractals: The Math Archive.

absalom's avatar

Thanks for the wealth of resources, @ETpro. Among the classes I listed, in which do you think I’d be most likely to encounter fractals? I am kind of torn between analytic geometry and complex analysis, which I imagine have some overlaps. I may as well email the professors.

@Trillian: Some are beautiful, yes, and fairly easy to grasp at a layman’s (i.e. non-mathematical) level. If you have free time and sufficient interest then I suggest this NOVA episode devoted to fractals. The whole thing is on YouTube and it’s totally easy to understand.

@ratboy: Yeah, I have, and naturally I don’t meet the prereqs because I’m an English major. I can still audit the course however and take from it whatever I can. Thanks also for the archive.

ETpro's avatar

@absalom It’s an easy enough study to undertake online that I wouldn’t worry about guiding the selection of classes by it, but by what will build best toward the field of endeavor you are targeting. You should already have the math you need. You are going to need computer programming though, because while the equation is quite simple, the complete set requires iterating it many millions of times.

LostInParadise's avatar

There is a connection between fractals and chaos theory. You may be primarily interested in fractals, but it is good to know how the two areas relate. I found a brief overview of this here As to the courses you mentioned, I would go with linear algebra. Fractals are non-linear, but it helps first to know about linear transformations. Linear algebra also talks about dimension, which plays an important role in fractals.

bobbinhood's avatar

If you’re looking for a class that will directly discuss fractals, you’re not likely to find it among that list. I have taken all of those classes except discrete, and it never came up. Since I have paged through a couple discrete texts, I’m fairly certain it won’t be in that class, either. Fractals are fascinating, but they’re not really part of any core classes.

I just looked through my geometry books. One of them includes an entire chapter on fractal geometry, while the other does not even mention it. If you really want to take a class on this, you could see if your school offers any upper-level geometry classes that actually include fractals. Though, I suspect that if they are included at all, they will be a topic that is covered for a couple days and not really a main part of the course.

I really don’t think you are going to find any college classes that focus on fractals (if you can manage to find one that mentions them at all). If you are set on going that route, you should talk to the chair of the math department. That person would have a good idea of the content of each course. However, you would probably be better off if you simply asked the chair which of the faculty would be best able to discuss fractals with you. Most math professors like it when someone is interested and asks good questions, so they would likely welcome the discussion.

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