Definition of FractalDate: 01/17/2005 at 08:15:14 From: Boris Subject: Fractals What is the definition of a fractal? I'm not sure what the definitive definition is from reading over the posts regarding fractals to date. I thought that maybe a circle would stretch the limits of the definition of a fractal? Date: 01/19/2005 at 12:07:50 From: Doctor Douglas Subject: Re: Fractals Hi Boris. The key idea in the definition of fractal is "self-similarity". What this means is that the object looks the same no matter what power magnifying glass you use to view it. In this sense a straight line is a fractal: if you enlarge it by a factor of 2X, or a factor of 10X, or a factor of 1000X, or 10^9X, it still looks like a straight line (of zero width). In fact it IS a straight line. So while it satifies the definition of a fractal in that it is self-similar (looking like a straight line no matter what magnification is used), it is not a particularly interesting "fractal". So to distinguish such familiar shapes as a (one-dimensional) line or a (two-dimensional) circular disk, often there is an another defining property to the concept of a fractal, namely, that fractals possess a non-integer dimension. Understanding this can involve some pretty sophisticated mathematics. But there is an introductory level (middle-school to high-school) explanation at Cynthia Lanius's website: Cynthia Lanius' Lessons: A Fractals Lesson http://math.rice.edu/~lanius/frac/index.html At a higher mathematical level, you can consult The Chaos Hypertextbook http://hypertextbook.com/chaos/ And for word definitions of the term "fractal", you can use the following: Fractal http://mathworld.wolfram.com/Fractal.html Fractal FAQ http://www.faqs.org/faqs/fractal-faq/ I hope that this helps. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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