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/ |
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