Timeline for Fractal dimension of 1D set, what if logN vs log(e) is a polygonal chain?
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| Mar 19, 2013 at 14:48 | vote | accept | mt_christo | ||
| Mar 12, 2013 at 22:33 | history | edited | mt_christo |
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| Mar 11, 2013 at 21:38 | vote | accept | mt_christo | ||
| Mar 12, 2013 at 22:33 | |||||
| Mar 5, 2013 at 13:38 | comment | added | Gerald Edgar | Perhaps begin with Mandelbot's paper, "How Long is the Coast of Britain?" | |
| Mar 5, 2013 at 10:56 | comment | added | Per Alexandersson | It sounds a bit like a multi-fractal, (en.wikipedia.org/wiki/Multifractal_system) which has "mixed" fractal dimensions. If your data do not have sufficient resolution, it might be an artifact that it eventually becomes zero. Now, some DLA-systems (en.wikipedia.org/wiki/Diffusion-limited_aggregation) have something similar happening in them, if I recall correctly. | |
| Mar 5, 2013 at 2:21 | answer | added | BSteinhurst | timeline score: 2 | |
| Mar 5, 2013 at 1:30 | comment | added | mt_christo | Sure - I am calculating number (N) of segments of equal length needed to cover the set as function of size of the segment (e). (explained here: en.wikipedia.org/wiki/Fractal_dimension) Then I plot it in double-log coordinates. Theoretically, slope of that curve as it approaches 0 is the fractal dimension of the set. But I have a finite set, and the overall curve is a polygonal chain. Basically, what I am asking is - what could be the intuition behind that? Any literature on such applications of fractal analysis? | |
| Mar 4, 2013 at 21:05 | comment | added | Robert Israel | Please explain more precisely what you mean. What are $N$ and $e$? If it's a finite set, it's certainly not a fractal. | |
| Mar 4, 2013 at 20:43 | history | asked | mt_christo | CC BY-SA 3.0 |