Talk:Fractal dimension

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[edit] Expand and make simpler please

Expand and make simpler please Alan2here 23:06, 5 November 2006 (UTC) I agree. Please define terms such as "attractor" for non-mathematicians. Also in figure 1 should r be l? —Preceding unsigned comment added by 71.164.135.92 (talk) 05:16, 20 December 2007 (UTC)

That's a tricky request, the picture is a little vague as stands, I'll try to clean that up. The attractor is the limit of the fractal, ie. the black triangles in the Seprinski gasket if we could iterate infinitely. I really don't think the major content of this article would be useful to describe to non-mathematicians, but the introductory paragraphs could do with a simplified layperson summary. I'll see what I can do. Nazlfrag (talk) 04:20, 31 December 2007 (UTC)
I've altered the first picture slightly, replacing r= with l= as per the main body of text and adding the values that equate to 1. As for a better description of attractors, I left that to the attractor article and linked the first occurrence to said article. As for a summary, the description in the second paragraph of the Koch curve is succinct, accurate and a better description than any I can think of. Perhaps an example with a real world fractal would help the non-mathematicians, though the concept of fractional dimensions is hard enough for mathematicians to get their heads around in the first place. Where is Mandelbrots amazing descriptive ability when you need it! The Fractal Geometry of Nature is comprehensible to nearly everyone, we should strive for that same level of clarity. Nazlfrag (talk) 05:52, 31 December 2007 (UTC)
Well, there are no (known) true fractals in nature. Fractal models for e.g. the coast of Norway may work fairly nicely for a while, but when you get down to subatomic levels, they're out. You run into trouble with quantum theory, I'm afraid. Similar obstacles hold for (the original) Brownian motion; and e.g. stock market behaviour suffers from another kind of "quantisation": You have no "movement" at all in the fractions of time where there is not a single transaction finished. Nevertheless, perhaps these three classical examples might serve as illustrations of the kind you're asking for (with an appropriate warning against overemploying the fracta models).
The second paragraph Koch curve unhappily uses "curve" in two different meanings, yielding the slightly paradoxical statement that the curve is not a curve. Apart from this minor matter, I agree with Nazlfrag's approval of that paragraph. JoergenB (talk) 15:46, 1 January 2008 (UTC)

[edit] Various definitions

[edit] Examples

I thnk the article is not bad. One suggestion for improvement: there are many definitions alluded to, and some discussed. Is it possible to show how differently the various definitions would quantify the fractal character of a given object? If there is some well-known (to mathematicians, at least) object where you could say, "Now by definition (1) we get 1.23 and by definition (2) we obtain 1.27, but definition (3) actually goes to infinity", or some such. —DIV (128.250.80.15 (talk) 06:45, 26 April 2008 (UTC))

[edit] Hausdorff

Can the parenthetic comment in the article "(which is more or less the Hausdorff dimension)" be elaborated on just a little more, perhaps in a footnote? —DIV (128.250.80.15 (talk) 06:48, 26 April 2008 (UTC))