Talk:Sierpinski triangle
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[edit] Java Code
I just compiled and ran the java code presented on the page. I got the following error:
- java SierpinskiTriangle
- java.lang.NoSuchMethodError: main
- Exception in thread "main"
[edit] About
About the Pascal's triangle you are not wrong, but the complete "triange" looks like:
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
0 0 0 0 0 0 1
. . 0 0 0 0 0 0 1 -5 15 -35
0 0 0 0 0 1 -4 10 -20 35 -56 84
. . 0 0 0 0 0 1 -3 6 -10 15 -21 28 -36 45 -55 . . .
0 0 0 0 1 -2 3 -4 5 -6 7 -8 9 -10
. . 0 0 0 0 1 -1 1 -1 1 -1 1 -1 1 -1 1 . . .
0 0 0 1 0 0 0 0 0 0 0 0 0 0
. . 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 . . .
0 0 1 2 1 0 0 0 0 0 0 0 0 0
. . 0 0 1 3 3 1 0 0 0 0 0 0 0 0 0 . . .
0 1 4 6 4 1 0 0 0 0 0 0 0 0
. . 0 1 5 10 10 5 1 0 0 0 0 0 0 0 0 . . .
1 6 15 20 15 6 1 0 0 0 0 0 0 0
. . 1 7 21 35 35 21 7 1 0 0 0 0 0 0 0 . . .
usw.
So you don't get:
#
# #
# #
# # # #
# #
# # # #
# # # #
# # # # # # # #
# #
# # # #
.
.
.
More you get like this:
.
.
.
# # # # # # # #
# # # #
# # # # # # # #
# # # # # # # #
# # # # # # # # # # # # # # # #. . . . .
1
1 1
1 2 1
1 3 3 1
# #
# # # #
# # # #
# # # # # # # #
. .
. .
. .
--217.233.252.114 10:58, 19 Mar 2004 (UTC)
[edit] 3D Sierpinskis
Take a look at Sv:Sierpinskitriangel. There you can find my 3D versions of the triangle. I have created the tool used to render the images. It is based on a three dimensional iterated function system. My technology to get the shadows there is probably new to the fractal scene. Please feel free to copy the images to here if you like. // Solkoll 01:29, 31 Jan 2005 (UTC)
- I think they should be also displayed on the english page.
- I can only guess what is written on the page but I can see you have written that the Hausdorff dimension is equal exactly 2. I Believe it should also be said on the english page. Also, It is noteworthy that a bijection to a square i an edge-first parallel projection of the bounding tetrahedron.
- Just out of curiousity, what shadow technology were you using? - Rainwarrior 18:33, 27 July 2006 (UTC)
[edit] Programcode to draw Sierpinski Triangles?
Would it not be appropriate to include some (recursive) programcode (e.g. a Java Applet) to draw Sierpinski Triangles? I have done so in the corresponding articles in the german and french language wikipedia. — Nol Aders 13:28, 24 November 2005 (UTC)
- I wrote an implementation of the Random-Convergence Sierpinski algorithm in C#, it doesn't use recursion, but is longer than the Java one posted (but unlike the Java one, this one compiles fine), should I post it? W3bbo 22:05, 2 August 2006 (UTC)
[edit] wrong redirect?
I get redirected here when searching for "Tetrix" what is a class of Grashoppers... Does that have a reason?
- According to the section "Analogs in higher dimension", a tetrix is a three-dimensional analog of the Sierpinski triangle. However, I agree that this is confusing for people looking for the insect, so I wrote a page at Tetrix saying that the word has two meanings. Unfortunately, we do not seem to have any information on the insect. Anyway, thanks for bringing this to our attention. -- Jitse Niesen (talk) 13:41, 16 January 2006 (UTC)
[edit] Construction
About the "Construction" part, I think that this sentence might be misleading:
"Shrink the triangle by 1/2, make three copies, and position the three copies so that each triangle touches the two other triangles at a corner (image 2)."
To me, making 3 copies would mean that there are 4 in total (including the original shrinked one). May be it should be change to "make 2 copies" or something.
Harris
- Good point, thanks. I changed it to "Shrink the triangle by 1/2, make two copies, and position the three shrunken triangles so that each triangle touches the two other triangles at a corner (image 2)." -- Jitse Niesen (talk) 06:08, 3 April 2006 (UTC)
[edit] Gasket or Carpet
I believe that the following passage should be moved to the Sierpinski carpet.
Sierpiński demonstrated that this fractal is a universal curve, in that any possible one-dimensional graph, projected onto the two-dimensional plane, is homeomorphic to a subset of the Sierpinski gasket. For curves that cannot be drawn on a 2D surface without self-intersections, the corresponding universal curve is the Menger sponge.
Well, let's see his articles:
Gasket: Sur une courbe dont tout point est une point de ramification. C. R. Acad. Sci. Paris 160(1915) 302-305
Carpet: Sur une courbe cantorienne qui contient une image biunivoque et continue de toute courbe donnée. (French) C. R. 162(1916), 629-632.
Please let me know if I am wrong. --Beaumont 17:25, 27 July 2006 (UTC)
- That's right. It should be at Sierpinski carpet. I came across that topic in a book called "The Beauty of Fractals" which also demonstrated specifically why the carpet could do this, but the triangle could not. - Rainwarrior 18:31, 27 July 2006 (UTC)
[edit] Tetrahederon
While the picture of the Sierpinski tetrahederon is cool, why is it on this page? - —The preceding unsigned comment was added by 64.56.112.130 (talk • contribs) 20:37, 27 October 2006 (UTC)
- Arguably, nowadays the Sierpinski triangle often means the object defined and studied in a N-dimensional setting (some sources on demand). Not a bad idea to have it here. --Beaumont (@) 20:58, 27 October 2006 (UTC)
- This page is about many forms of the sierpinski triangle, so any material about the sierpinski tetrahedron belongs here. - Rainwarrior 06:59, 28 October 2006 (UTC)
- The pictured item labeled 'Sierpinski tetrahedron', however cool looking, actually has 5 sides (a rectangular pyramid) User:Sarujin 8:20 AM, 11 November 2006 (UTC)
