Hans W Borchers
2018-Sep-15 19:38 UTC
[R] How can I know the Hausdorff dimensions of fractals in the 'fractalcurve' function of package 'pracma'?
> Dear Dr. Hans W. Borchers,This is a public mailing list; do not address specific people here, everyone can read and (possibly) answer your questions. And please send e-mail in plain text format, not as HTML.> I'm using your 'pracma' package. It is very useful. May I have a small > question for the 'fractalcurve' function? How can I know the Hausdorff > dimension for every option below? > c("hilbert", "sierpinski", "snowflake", "dragon", "triangle", > "arrowhead", "flowsnake", "molecule") > For the "dragon" option, its Hausdorff dimension is log(4)/log(2) = 2. > For the others, what are the Hausdorff dimensions?I don't know. Have you tried the *fractaldim* package to find at least a plausible numerical value for the Hausdorff dimension?> I have found the list of some fractals by Hausforff dimensions. > I don't know which in the above option corresponds to which in Wikepedia.Guess you mean the "List of fractals by Hausdorff dimension". Well, "hilbert" is obviously the Hilbert curve and has a Hausdorff dimension of 2 -- because it is a 'space-filling' curve.[^1] Otherwise, use `fractalcurve()` to generate plots of the fractal curves and compare with the pictures shown on the Wikipedia page. Not all the curves may be present on this list, though.> Thanks a lot! > Best wishes, > Peijian Shi--- [1] By the way, I doubt your estimation that the dragon curve has Hausdorff dimension 2; it looks more like 1.5236.