[R] How can I know the Hausdorff dimensions of fractals in the 'fractalcurve' function of package 'pracma'?

Hans W Borchers hwborcher@ @end|ng |rom gm@||@com
Sat Sep 15 21:38:22 CEST 2018

> Dear Dr. Hans W. Borchers,

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> 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.

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