Talk:Sierpiński triangle

message: 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)
replies: text: 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)

text: You can also run applets from the command line using the appletviewer(1) command, on *nix or Windows. - SamB (talk) 17:02, 23 June 2010 (UTC)
thread_title: Java Code

message: 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)
thread_title: About

message: 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)
replies: text: 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)
thread_title:  Programcode to draw Sierpinski Triangles? 

message: 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)
thread_title:  wrong redirect? 

message: 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)
thread_title:  Construction 

message: 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)
replies: text: 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)
thread_title:  Gasket or Carpet 

message: 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)
thread_title:  Formula? 

message: 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)
replies: text: See Talk:Sierpinski number. I haven't examined "Sierpinski triangle". PrimeHunter 12:10, 6 January 2007 (UTC)
thread_title: Naming:  Sierpiński versus Sierpinski

message: 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)
replies: text: 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)
thread_title: Pen and Paper

message: 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)
replies: text: 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)

text: 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)
replies: text: 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)
thread_title:  Initial Description 

message: 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)
thread_title: Physical model with clay

message: 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)
thread_title:  Image not aligned 

message: I have an image of the "Sierpiński triangle-based Pyramid" as seen from above and  one as seen in 22.5°x22.5°x0° 3D. Are those considered appropriate images?— Supuhstar  * § 18:16, 30 June 2008 (UTC)
thread_title:  for "Analogs in Higher Dimention" 

message: Title says it all.  As long as it's not genuinely horrible or pornographic, we'd like to see it.
:what?? Tommy has a great username (talk) 19:09, 3 January 2019 (UTC)
thread_title: Well, go ahead and post it

message: This is problem from Physics of particle scattering. 
http://imonad.com/blog/wp-content/uploads/2008/07/img520.jpg
Also some POV code to reproduce the results.
http://imonad.com/blog/2008/07/chaotic-scattering-with-povray/
I consider this to be "higher dimension" (actually 3d) because you can look around it.
Can somebody add this image at the appropriate place in the text?  —Preceding unsigned comment added by Aquarin (talk • contribs) 08:30, 1 August 2008 (UTC)
thread_title:  I have image of "higher dimension" Sierpisnki appearing in the Chaotic Scattering problem 

message: What's the proper spelling in the context of "Analogs in higher dimension"? I'd have said 'analogue'. Tophtucker (talk) 16:41, 8 April 2009 (UTC)
replies: text: There's no context, the difference in the spelling of "analog" is dependent upon whether you're an American writer or a British one. "Analog" is considered the standard English spelling, while "analogue" is considered the "Commonwealth English" spelling. (reference: wiktionary) (I consider the American spelling "standard" because my perception is that American English is the more influential language on a global scale, and thus assume more people use it, if you disagree, kindly replace the word standard with the word American, because I don't care enough to argue about it here) (Astrocom (talk) 07:45, 29 June 2010 (UTC)
thread_title:  Analog or Analogue? 

message: I was just reading the Blood type article and noticed that the Red blood cell compatibility table and the Plasma compatibility table look like the second and first approximations of the sierpinski triangle (when rotated). Is this worth mentioning in the article, e.g in a notes/in nature/... section ? what do you think ? --George (talk) 05:37, 5 October 2009 (UTC)
replies: text: I don't agree, the tables do not look like approximations to the Sierpinski triangle, more like a square with a diagonal. /Pontus (talk) 18:58, 5 October 2009 (UTC)

text: Ok, sorry, I didn't look at the tables, just the charts. I think one could express a generalization of this in the following way. Let Q<SUB>n</SUB> be the directed n-dimensional hypercube graph. (The vertices are 0-1-sequences of length n, and there is a directed edge from x to y if x and y differs in exactly one position, at which x is 1 and y is 0.) Then the 0-1-matrix representing the partial order defined by reachability between the vertices of Q<SUB>n</SUB> (or, equivalently, the adjacency matrix of the transitive closure of Q<SUB>n</SUB>, with loops added at all vertices), with rows and columns of the matrix ordered by lexicographical order of the vertices, equals the (n-1)-st approximation of the Sierpinski triangle (viewed as a 0-1-matrix). I haven't found a reference for this. /Pontus (talk) 19:30, 6 October 2009 (UTC)

text: I realized that it is easier to define the partial order using the binary AND as you did: x≤y if (x AND y) = x, where x and y are integers from 0 to 2<SUP>n</SUP>-1. /Pontus (talk) 20:29, 6 October 2009 (UTC)
thread_title:  worth mentioning ? 

message: Are there solid references?
dino (talk) 15:35, 5 October 2009 (UTC)
thread_title: References?

message: What does the novel Infinite Jest have to do with this? Why is it in the See Also section? 129.120.8.194 (talk) 17:26, 15 October 2009 (UTC)
replies: text: removed. - Altenmann >t 17:38, 15 October 2009 (UTC)
thread_title:  Infinite Jest 

message: I have a small amount of Original Research on this subject, far too small to ever be published as anything but commentary on the topic, and then, who would publish commentary on the topic? What should I do with it? I'm not a professor or a grad student, I don't have a sub-domain on a .edu site, so I have no way of putting this out in anyway that would be considered a reliable source.
If anyone is interested, I can elaborate on my (very small) amount of knowledge to add to the topic. (Astrocom (talk) 07:41, 29 June 2010 (UTC)
thread_title:  Original Research? 

message: In regard to this , I'm not questioning the reliability of the source. I do think however that this is a sort of an interesting trivia fact that can be put into the article but doesn't necessarily belong in the lede. But it's not a big deal either way.Volunteer Marek (talk) 21:58, 28 February 2011 (UTC)
replies: text: It belongs wherever it is that we assign credit for its "discovery" to Sierpinski. Right now that's in the lede. But I agree that we aren't following MOS:LEDE in that the lede contains information not elaborated on in the rest of the article — not just the Cosmati mosaics but Sierpinski's role. —David Eppstein (talk) 23:12, 28 February 2011 (UTC)
replies: text: Well, the thing is that fractal patterns occur in nature quite often, and art is often based on nature (particularly in mosaics) so it's not surprising that these fractals can be found in artistic works from long ago. And that's interesting. But that doesn't mean that the Cosmati mosaic "discovered" the Sierpinski triangle in any kind of mathematical sense, anymore than some sea snails "discovered" the golden ratio.Volunteer Marek (talk) 23:23, 28 February 2011 (UTC)

text: So only mathematicians are capable of making discoveries, and everyone else is at the intellectual level of a sea snail? That seems a very strange perspective on intellectual progress. I'd advise you not to say so in front of any artists. —David Eppstein (talk) 23:57, 28 February 2011 (UTC)
replies: text: So only mathematicians are capable of making discoveries, and everyone else is at the intellectual level of a sea snail? - That's right.Volunteer Marek (talk) 01:00, 1 March 2011 (UTC)

text: No, ok, seriously, though I do know some mathematicians who take that view, there is a difference between a "mathematical discovery" (defining and characterizing a set) and a "artistic discovery" (finding a cool looking pattern for your mosaic) even if we're talking about the same thing. And yes, it is mathematicians who mostly make the "mathematical discoveries".Volunteer Marek (talk) 01:04, 1 March 2011 (UTC)
replies: text: Ok, but is this article only about the mathematics of the Sierpinski triangle? And if so, where is that other article that covers the pattern in all its other aspects? And in any case I don't think "discovery" is the right word for what happens when a mathematician analyzes things that were already known (but not analyzed) to other people. —David Eppstein (talk) 01:13, 1 March 2011 (UTC)
thread_title:  cosmati mosaic 

message: Why, what, where, and how does this article need additional citations for verification? Hyacinth (talk) 16:04, 28 October 2011 (UTC)
replies: text: Most of the construction section, all of the properties section, and all of the analogues section (that is to say, most of the article) have no footnotes or other forms of referencing indicating which of the stated facts come from which source. The few sources we have are not of the highest quality — we should easily be able to get published books for most of this material, rather than self-published web sites, which are already duplicated in the external links section. And the existing external links section is too long — many of those links should be cut. —David Eppstein (talk) 16:17, 28 October 2011 (UTC)
thread_title: Additional citations

message: Hello guys,
here's a javascript code i've just made for the fractal, fully working on the html5 canvas:
http://jsfiddle.net/Saturnix/2P7WT/
Just call fractal_iteration(); for each iteration you want to do.
Hope someone may post it :)
Thanks!  — Preceding unsigned comment added by 93.50.239.209 (talk) 01:04, 21 April 2012 (UTC)
thread_title:  Javascript code 

message: I know of at least two other methods to generate this pattern that aren't on the page.  The first is created by using a binary tree, and is related to Pascal's triangle:
#Start with a single point
#Branch down to the left and right by a fixed amount and create a new point at each end
#From each point, branch to the left and right, omitting any branches which would end up landing in the same place
#Repeat
This will ultimately lead to this pattern.  You can see this demonstrated here (Starting at about 2:00)
Another similar method creates not one, but 6 Sierpinski triangles in a hexagonal arrangement:
#Start with a single equilateral triangle
#Add another triangle to each face of the first
#Add more triangles to each face of the last triangles, all the same size
#Continue this pattern, but do not generate triangles where two of them would overlap.
You'll end up with 3 triangles at 120 degree angles to each other which all start with your original triangle at the tip, and 3 more at 60 degrees to those in which your original triangle serves upside-down as the first of the gaps (your 3 second-tier triangles forming the tips).  Don't have a picture or video for this one, but you can try it out yourself with pen and paper.  Lurlock (talk) 04:29, 13 February 2014 (UTC)
thread_title:  Other means of generating 

message: I have generated a Sierpinski Triangle using a single line in a fractal curve. Demonstration of this method is on my JsFiddle: http://jsfiddle.net/alancnet/exu7T/
I believe this should be part of the article, since it shows how the triangle can appear from a completely different algorithm.
:See Sierpiński arrowhead curve. I agree, this should be in the article; I just added it. —David Eppstein (talk) 22:49, 19 March 2014 (UTC)
thread_title:  Fractal Curve, SVG and JavaScript 

message: An ex-editor recently added three sub-sections to the  section, none of which are grammatical or make much sense:
* (1.8) Sierpinski Tautology Map
* (1.9) Use of Collage Theorem
* (1.10) Sierpinski Gasket
While they've put much work into these edits, I doubt whether any reader will find them helpful, nor even particularly comprehensible.  Certain grammatical faults cause me to suspect that the editor's first language may not be English, which may contribute to the obscurity of some sentences.
So, following the precept "Be bold!", I'm removing these additions in their entirety.  Supposing that the person in question still wants to contribute to the article under those headings, they're welcome to contact me for help in making their meaning clear.  yoyo (talk) 12:29, 7 July 2018 (UTC)
thread_title:  Nonsensical additions to "Constructions" 

message: Sierpinsky Triangle is used for motion capture tracking:
https://patents.google.com/patent/WO2013009547A1/en
https://mathoverflow.net/questions/233998/unexpected-occurences-of-the-sierpinski-triangle
https://www.quora.com/Why-is-a-Sierpinski-triangle-pattern-used-on-some-capture-suits
guess it deserves a mention in the article.  — Preceding unsigned comment added by NikitaSadkov (talk • contribs) 19:51, 21 September 2018 (UTC)
thread_title:  Motion Capture Pattern 

message: is it just me or does it look kinda like a triforce symbol? Tommy has a great username (talk) 19:16, 3 January 2019 (UTC)
thread_title:  triforce 

message: The Sierpinski triangle can be realized using an LC network, that is, by constructing each level with inductors and interconnecting the levels via capacitors. The resulting resonant network has unique, apparently paradoxical, properties since in the limit of infinite iterations it is dissipative even though it is built using purely reactive elements.
Ruiz PA
"Power dissipation in fractal Feynman-Sierpinski AC circuits"
 When constructed up to a finite number of iterations, such kind of a resonator can be used to obtain high-dimensional dynamics even from elementary electronic circuits, involving a single transistor as the only active and non-linear element. 
* The splendid generative potential of the Sierpinski triangle  ( Lminati (talk) 15:22, 12 March 2019 (UTC)
thread_title:  Proposed addition regarding construction: "LC resonant network"

message: In the parapraph "Analogs in Higher Dimensions" it is said that the surface area remains unchanged  upon iteration while the volume approaches zero, which is both correct using the formulae. But the next sentence states  "The limit of this process [i.e. the iteration] has neither volume nor surface...". How can this be understood in a way that it does not contradict with what was just shown before? --193.222.161.35 (talk) 12:57, 18 December 2019 (UTC)
replies: text: Each finite iteration has the same surface area, but the limiting object (which is not equal to any of the finite iterations) does not.  There is no contradiction, just a (surprising?) fact about what properties are or are not preserved by limits. --JBL (talk) 01:55, 6 February 2020 (UTC)
thread_title: higher dimensions

message: The text below the animation of the fractal tree outlining the sierpinski triangle says:
A Sierpinski Triangle is outlined by a fractal tree with three branches forming an angle of 60° between each other. If the angle is reduced, the triangle can be continuously transformed into a fractal resembling a tree.
I believe the text should be:
A Sierpinski Triangle is outlined by a fractal tree with three branches forming an angle of 120° between each other. If the angle is reduced, the triangle can be continuously transformed into a fractal resembling a tree.
If the three branches of the fractal tree are only 60° between each other, you get the following figure after 3 iterations: https://haan.lu/sierpinski.png  
— Preceding unsigned comment added by 2a06:4944:8fc:4400:1d5:72ae:b9e0:19f (talk) 11:57, 8 April 2021 (UTC)
thread_title:  Wrong angle for fractal tree version