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### What Kind of Math are Fractals?

```Date: 10/23/2004 at 20:16:37
From: Lauren
Subject: What branch of mathematics do fractals belong?

Can you tell me what branch of mathematics includes fractals?

```

```
Date: 10/25/2004 at 17:45:43
From: Doctor Douglas
Subject: Re: What branch of mathematics do fractals belong?

Hi Lauren.

Thanks for writing to Dr. Math.  Excellent question!

If I interpret your question literally, then my answer is this:
fractals are geometric objects in the same way that lines and
triangles and spheres and ellipses are geometric objects.  Each of
these geometric figures possesses certain properties that make them
useful or interesting for one reason or another.  For example, the
interior angles of a triangle add up to 180 degrees.  Or, the sphere
gives the maximum volume enclosed for a given surface area.  The
special property of fractals is that they are each "self-similar" in
some way:

What is a Fractal?
http://mathforum.org/library/drmath/view/54525.html

However, you may be more likely to encounter fractals from other
branches of mathematics, just as you may encounter circles in branches
of mathematics other than geometry (for example, you might use circles
when you work with imaginary numbers in complex analysis, or if you
use the unit circle in trigonometry).  Some of the branches of
mathematics that give rise to fractal objects are the following:
differential equations and dynamical systems theory (e.g. "strange
attractors"), measure theory (Cantor set), and complex analysis
(Mandelbrot set).

You may also encounter fractals in applications of mathematics, such
as image compression, or computer art, or a whole host of scientific
and engineering problems:

Fractal Image Compression
http://mathforum.org/library/drmath/view/54530.html

Fractals in Real Life
http://mathforum.org/library/drmath/view/54539.html

I hope that this answers your question.  Feel free to write back if
you need more help with this.

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Fractals

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