Hausdorff dimension: Difference between revisions
Jump to navigation
Jump to search
imported>Hendra I. Nurdin mNo edit summary |
imported>Jesse Weinstein (move categories to metadata page) |
||
| Line 1: | Line 1: | ||
{{subpages}} | {{subpages}} | ||
In [[mathematics]], the '''Hausdorff dimension''' is a way of defining a fractional area for all dimensional figures such that the dimension describes partially the way that an area moves in the space around it. For example, a [[plane (geometry)|plane]] would have a Hausdorff dimension of 2. However, it would not make sense to give the [[Sierpinski triangle]] [[fractal]] a dimension of 2, since it does not fully occupy the 2-dimensional realm. Therefore, its Hausdorff dimension describes it mathematically, creating a relationship between the number of new self-similar sections and their scale. | In [[mathematics]], the '''Hausdorff dimension''' is a way of defining a fractional area for all dimensional figures such that the dimension describes partially the way that an area moves in the space around it. For example, a [[plane (geometry)|plane]] would have a Hausdorff dimension of 2. However, it would not make sense to give the [[Sierpinski triangle]] [[fractal]] a dimension of 2, since it does not fully occupy the 2-dimensional realm. Therefore, its Hausdorff dimension describes it mathematically, creating a relationship between the number of new self-similar sections and their scale. | ||
Revision as of 01:36, 22 December 2007
In mathematics, the Hausdorff dimension is a way of defining a fractional area for all dimensional figures such that the dimension describes partially the way that an area moves in the space around it. For example, a plane would have a Hausdorff dimension of 2. However, it would not make sense to give the Sierpinski triangle fractal a dimension of 2, since it does not fully occupy the 2-dimensional realm. Therefore, its Hausdorff dimension describes it mathematically, creating a relationship between the number of new self-similar sections and their scale.