请输入您要查询的字词:

 

单词 Fractal
释义

fractal


There are several ways of defining a fractalMathworldPlanetmath, and a reader will need to reference their source to see which definition is being used.

Perhaps the simplest definition is to define a fractal to be a subset of n with Hausdorff dimensionMathworldPlanetmath greater than its Lebesgue covering dimension. It is worth noting that typically (but not always), fractals have non-integer Hausdorff dimension. See, for example, the Koch snowflakeMathworldPlanetmath and the Mandelbrot setMathworldPlanetmath (named after Benoit Mandelbrot, who also coined the term “fractal” for these objects).

A looser definition of a fractal is a “self-similar object”. That is, a subset or n which can be covered by copies of itself using a set of (usually two or more) transformationMathworldPlanetmath mappings. Another way to say this would be “an object with a discrete approximate scalingMathworldPlanetmath symmetryMathworldPlanetmathPlanetmath”.

See also the discussion near the end of the entry Hausdorff dimension (http://planetmath.org/HausdorffDimension).

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 9:58:59