Content deleted Content added
draft page for fractal measure |
applications |
||
Line 1:
'''Fractal measure''' is a generalization of the concepts of length, area, and [[volume]] to non-[[integer]] dimensions, especially in application towards [[fractal]]s. There is no unique fractal measure, in part although not entirely due to the lack of a unique definition of [[fractal dimension]]; the most common fractal measures include the [[hausdorff measure]] and the packing measure, based off of the [[hausdorff dimension]] and [[packing dimension]] respectively.<ref>http://www.diva-portal.org/smash/get/diva2:22333/FULLTEXT01</ref> Fractal measures are measures in the sense of [[measure theory]], and are usually defined to agree with the ''n''-dimensional [[Lebesgue measure]] when ''n'' is an integer.<ref>https://link.springer.com/chapter/10.1007/978-1-4757-2958-0_1</ref> Fractal measures find application in the study of fractal geometry, as well as in [[physics]] and [[biology]] through the study of [[fractal derivative]]s.<ref>{{cite journal |first=W. |last=Chen |title=Time–space fabric underlying anomalous diffusion |journal=Chaos, Solitons and Fractals |volume=28 |issue= 4|pages=923–929 |year=2006 |doi= 10.1016/j.chaos.2005.08.199|url=|arxiv=math-ph/0505023 |bibcode=2006CSF....28..923C |s2cid=18369880 }}</ref> Fractal measure can be used to define the fractal dimension or vice versa.
==Hausdorff measure==
| |||