Talk:List of fractals by Hausdorff dimension

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2 october 2006. Translation and Transfer from the french article, which was more complete. Prokofiev (Alexis Monnerot-Dumaine).

Contents

[edit] penrose tilings

Could you explain shortly how to determine the Hausdorff dimension of the Penrose tiling? In what sense it can be seen as a true fractal? At some scale its geometry is no longer "fine". The citation has no details. Beaumont 21:02, 2 October 2006 (UTC)

The best is to have a look at the external link (bottom of page).Prokofiev2 3 October 2006 (UTC)
Thanks! I've changed it into a reference. Beaumont 15:56, 4 October 2006 (UTC)

[edit] Coastline of Norway

Felt a fleeting temptation to link it to Slartibartfast... AnonMoos 19:20, 9 December 2006 (UTC)

[edit] z-order curve

I believe that this is discontinuous and thus not a "curve", yet I agree it belongs in this context as it shares other important properties with these curves. See <http://cap-lore.com/MathPhys/Zorder/> for discontinuity argument and also non-differentiability. NormHardy 19:18, 26 December 2006 (UTC)

[edit] 'swiss cross fractal'

I'm a little puzzled both by the inclusion of this shape and it's linked picture. The limit of the fractal described is just a square. It seems a little strange to consider this a fractal. I know some 'fractal curves' cover the unit square in the limit, but these have other interesting properties in general (continuity, parametrization of the square..) I'm not sure the 'greek cross fractal' needs to be mentioned so much given that it doesn't seem to be a particularly interesting shape in any obvious way. Furthermore, the picture of the 2d greek cross fractal shows an early stage approximation to it. As mentioned the limit would just be a square. Obviously it's not possible to represent the limit strictly, but I find the picture is a little misleading given the above points. A mathematically unsophisticated reader might think the 'fractal' has some fine structure not present in the square. I'll review the page on this fractal and consider changing or removing it from here.

[edit] Definition

Several of the listed examples (like the Smith-Volterra-Cantor set, the Mandelbrot set, and the space-filling curves) seem to have the same Hausdorff dimension and topological dimension, and therefore they don't meet the definition of fractal at the beginning of the article. Maybe the definition should be changed to something more like the one on the fractal page. —Preceding unsigned comment added by 160.39.28.117 (talk) 07:18, 30 November 2007 (UTC)

Ok
You are right for the Mandelbrot set (corrected, the interresting part is the boundary). For the space-filling curves, the topological and the fractal dimension are actuallay different. Prokofiev. 7 dec 2007. —Preceding unsigned comment added by Prokofiev2 (talk • contribs) 17:19, 7 December 2007 (UTC) Reformatted —DIV (128.250.80.15 (talk) 02:55, 28 April 2008 (UTC))

[edit] Deterministic

The whole point of so-called 'natural, random' aggregates etc. is that they are products of deterministic chaos. The classification used here is misleading. —DIV (128.250.80.15 (talk) 02:57, 28 April 2008 (UTC))

[edit] Why does the coastline of Norway have more dimesions than the coastline of Britain?

It seems like they would have the same value, as they are both coastlines.128.232.241.115 (talk) 00:38, 10 May 2008 (UTC)

It has been mesured (see reference on the article). Coastlines are more or less irregular and Norway's westcoast is particularily irregular.Prokofiev2 (talk) 08:32, 13 May 2008 (UTC)