tea.mathoverflow.net - Discussion Feed (Question about a Reference)

Daniel Krenn comments on "Question about a Reference" (8147)

Daniel Krenn — Fri, 06 Aug 2010 05:19:44 -0700

Ok, thanks. I posted it at MO.

José Figueroa comments on "Question about a Reference" (8145)

José Figueroa — Fri, 06 Aug 2010 04:53:38 -0700

It seems like a reasonable question to me.

Andrew Stacey comments on "Question about a Reference" (8144)

Andrew Stacey — Fri, 06 Aug 2010 04:53:30 -0700

I vote that that qualifies!

Daniel Krenn comments on "Question about a Reference" (8143)

Daniel Krenn — Fri, 06 Aug 2010 04:49:00 -0700

The Problem is the following.

Let $KS$ be the Koch snowflake. This fractal has an iterated function system (IFS) of the form
$$ KS = \bigcup_{0 \leq k \leq 6} f_k(KS) $$
with
$$ f_0(z)=1/\sqrt{3} e^{i\pi/2} z $$
and for $0 < k \leq 6$
$$ f_k(z)=1/\sqrt{3} e^{ik\pi/3} + 1/3 z. $$

This seems to be commonly known. The Webpage [1] shows this behavior. Does anybody know a reference (e.g. article in a journal) where I can found this IFS?

I tried the following things.
- I have not found any reference by a extended web and library search.
- I talked to people working with fractals. They said, it is commonly known and should be written down somewhere, but none of them found a reference (although one did a extensive search in the library).
- I contacted the author of [1]. He said, that he has taken it from Mathworld [2].
- I looked up most of the references at the bottom of [2]. I found nothing.
- Especially, nothing can be found in Koch [3] and Cesàro [4].
- Some weeks ago I posted it in a German speaking newsgroup (de.sci.mathematik). No result (reference) was found.

[1] http://www.meden.demon.co.uk/Fractals/kochsnowflake.html
[2] http://mathworld.wolfram.com/KochSnowflake.html
[3] Koch, H. von. "Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes planes." Acta Math. 30, 145-174, 1906.
[4] Cesàro, E. "Remarques sur la courbe de von Koch." Atti della R. Accad. della Scienze fisiche e matem. Napoli 12, No. 15, 1-12, 1905. Reprinted as §228 in Opere scelte, a cura dell'Unione matematica italiana e col contributo del Consiglio nazionale delle ricerche, Vol. 2: Geometria, analisi, fisica matematica. Rome: Edizioni Cremonese, pp. 464-479, 1964.

Pete L. Clark comments on "Question about a Reference" (8138)

Pete L. Clark — Fri, 06 Aug 2010 03:20:15 -0700

As long as you have exercised at least a little diligence in trying to track down references on your own (e.g. wikipedia, google), I would think that such a question would very probably be acceptable on MO.

Harry Gindi comments on "Question about a Reference" (8137)

Harry Gindi — Fri, 06 Aug 2010 03:15:19 -0700

Give us more information about the question so we can decide...

Just write the question here on meta, and we'll approve or disapprove (if we disapprove, I'm sure you can ask on math.stackexchange.com).

Daniel Krenn comments on "Question about a Reference" (8136)

Daniel Krenn — Fri, 06 Aug 2010 03:08:10 -0700

Am I allowed to ask a question about finding a reference (paper, book) about a specific problem in MO? I have looked a lot and not found it until now.