Top Document: Fractal Frequently Asked Questions and Answers Previous Document: Learning about fractals Next Document: Chaos See reader questions & answers on this topic!  Help others by sharing your knowledge Q2: What is a fractal? What are some examples of fractals? A2: A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reducedsize copy of the whole. Fractals are generally selfsimilar and independent of scale. There are many mathematical structures that are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set, and Lorenz attractor. Fractals also describe many realworld objects, such as clouds, mountains, turbulence, and coastlines, that do not correspond to simple geometric shapes. Benoit Mandelbrot gives a mathematical definition of a fractal as a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension. However, he is not satisfied with this definition as it excludes sets one would consider fractals. According to Mandelbrot, who invented the word: "I coined _fractal_ from the Latin adjective _fractus_. The corresponding Latin verb _frangere_ means "to break:" to create irregular fragents. It is therefore sensible  and how appropriate for our needs!  that, in addition to "fragmented" (as in _fraction_ or _refraction_), _fractus_ should also mean "irregular," both meanings being preserved in _fragment_." (_The Fractal Geometry of Nature_, page 4.) User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Fractal Frequently Asked Questions and Answers Previous Document: Learning about fractals Next Document: Chaos Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: stepp@marshall.edu
Last Update March 27 2014 @ 02:11 PM
