Talk:Sierpiński 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"
- —Preceding unsigned comment added by Russoc4 (talk • contribs) 10:16, 8 April 2006
- The program in the article is an applet, you can't run it with java.exe. You need to first create an HTML page (.html file) with the applet in it and view it either from a web browser or with appletviewer.exe. I think the code in the HTML page is:
<html>
<applet code="javaApplet.java">
</html>
- Zchenyu 16:03, 29 July 2007 (UTC)
- Most Java IDEs have an option to run as an applet, also. There should hopefully be no need to make a webpage just to run it. - Rainwarrior 21:08, 29 July 2007 (UTC)
[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)
Also, shouldn't "Repeat step 2 with each of the smaller triangles (image 3 and so on)" instead just be "Repeat step 2 (image 3 and so on)"?
In other words, you don't need to repeat with each of the three triangles, but can repeat with the full triangle instead. It seems that approach is cleaner/simpler as it involves a simple loop instead of a recursion.
Tom Dibble 00:01, 15 September 2007 (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)
-
- It seems to say "pyramid" now on the picture, but I added a note to the text nearby that there is also a pyramid construction. - Rainwarrior 21:14, 29 July 2007 (UTC)
[edit] Formula?
Doesa anyone have a series/sequence formula for the total number of triangles, as well as a formula for finding the area of a triangle at stage "n", And is there a way to do this without using the recursive or "iterated function" method?--AeomMai 22:24, 3 January 2007 (UTC) Once you learn it, it is REALLY easy!
area - where n is iteration number - 0 is a triangle B is area of original triangle A = B * (3/4)^n Every time you iterate, you are basically multiplying the area by 3 but you are increasing the size of the entire triangle by 4
X
XOX
X XOOOX
X -> XOX -> XOXOXOX
1 -> 3/4 -> 9/16 -> 27/64 ...
number of triangles (black) -> 3^n
number of triangles (white) -> 4^n - 3^n
total area -> 4^n VentusIgnis 16:24, 18 June 2007 (UTC)
[edit] Naming: Sierpiński versus Sierpinski
Apparently this is named after Wacław Sierpiński, so why doesn't the spelling reflect that accurately here, as it does for Sierpiński's constant and Sierpiński curve? Does this need fixing up? —DIV 128.250.204.118 03:40, 6 January 2007 (UTC)
- See Talk:Sierpinski number. I haven't examined "Sierpinski triangle". PrimeHunter 12:10, 6 January 2007 (UTC)
[edit] Pen and Paper
I remember a math teacher teaching a class on probability or chaos or something; asking us for some pairs of random numbers, plotting the medians of each pair, and ending up with a sierpinski triangle... it was a very dramatic demonstration... can anyone recall and describe this process? I think it'd be a good inclusion for an encyclopedia article. 24.68.135.133 02:21, 28 July 2007 (UTC)
- There is a "chaos game" described in the article which involves randomness and midpoints (you take a random point, and then find the midpoint between that one and one of three fixed points, then repeat the process). Does it describe what you are talking about? - Rainwarrior 03:42, 28 July 2007 (UTC)
[edit] Initial Description
The initial description of the method of construction DOESN'T describe why the middle hole doesn't get filled in. I, personally, don't understand why it doesn't get filled in. My ONLY experience of the Sierpinski Triangle is from THIS article. So maybe that says something. :-) Martin Packer 11:40, 9 November 2007 (UTC)
- Maybe step 2 in Construction should be reformulated. Step 2 replaces each triangle with 3 triangles of half the height, positioned inside the original triangle so they touch eachother at a corner (but not at a side). This positioning is part of the definition and it leaves a hole in the middle. PrimeHunter 12:23, 9 November 2007 (UTC)
I think that's MUCH better. The only tweak one might do is to spoon-feed the reader as to WHY that leaves a hole in the middle. Martin Packer 12:53, 9 November 2007 (UTC)
- I'm not sure what you refer to with WHY. Do you mean why Sierpinski studied that form? I don't know. Do you want an explanation saying that 1/2 height and 1/2 width gives 1/4 the area, so it takes 3 smaller triangles and 1 hole of the same size to fill out the original triangle? Do you want a geometric explanation why the hole not only has the same size but also the same triangle form (upside down) as the 3 triangles? PrimeHunter 14:07, 9 November 2007 (UTC)
- Thanks PrimeHunter: I really mean "why the step leaves the hole in the middle". It IS, I would agree, slightly spoonfeeding but the holes ARE a major feature of the triangle. Martin Packer 19:39, 9 November 2007 (UTC) (who claims to be a reasonable cipher for a layperson in this topic)
[edit] Physical model with clay
I would like to propose that an appropriate external link might be to this page, which shows one way to model the Sierpinski triangle physically, using an iterative process with modeling clay. I wrote the link in question, so I will not add it to the main article myself. But perhaps other editors would agree that it could be a useful addition to the page. —Preceding unsigned comment added by Oskay (talk • contribs) 22:12, 10 December 2007 (UTC)
[edit] Image not aligned
The Sierpinski triangle image is not horizontally aligned, which breaks its symmetry. You can better see this at full size. —Preceding unsigned comment added by Alphachapmtl (talk • contribs) 17:12, 19 January 2008 (UTC)
