Talk:Sierpiński carpet

Image format

The previous version of the article contained http://meta.wikipedia.com/upload/Sierp.jpg

This JPEG image has coloring artifacts around the edges of elements (i.e. everywhere) and is over 250 kibibytes in size. I have created a different version in PNG format that takes less than 2 percent of the original file's size and uploaded it to the Meta-Wikipedia, saving Bomis over 250 KiB per hit. (Isn't deflation wonderful?) --Damian Yerrick

It is. The previous version was mine, but I don't regret having elicited a more economic carpet :)). Your triangle is nice too. -- Piotr Gasiorowski

Number of iterations

Aren't there more than four iterations there?

How silly of me! The image is 729 pixels wide, the fractal has a reduction factor of 3, and log[3](729) = 6 iterations.

I've updated the image's caption to reflect this.

--Damian Yerrick

Accurate images

The article is about the Sierpinski carpet itself, not about different ways of constructing it. The existing images (Sierpinski.png and Fractal squares.png) contain artifacts that are not part of the carpet, and are not accurate because of anti-aliasing. Also, there is no reason to include more than one image. For these reasons, I created one new, pixel-perfect image (SierpinskiCarpet6.png) to replace the old ones.
—Herbee 17:05, August 20, 2005 (UTC)

Both the images you removed from Sierpinski carpet where clear images, if sized correctly. See Wikipedia:Picture tutorial. Hyacinth 21:20, 20 August 2005 (UTC)

Thanks, I know all about stretching images. I didn't say the old images were unclear, whatever "clear" means in this context. I am saying that Fractal squares.png is misleading: the image contains spurious black lines, and has smallest holes of different sizes.

The other image, Sierpinski.png, actually gives a good impression of the Sierpinski carpet. I may have removed it too quickly. To fix the article, I will include images like my SierpinskiCarpet6.png to show the construction process.

—Herbee 16:35, August 21, 2005 (UTC)

Thanks for the note. "Unclear" was your word, but I do prefer your depiction of the first few iterations. Hyacinth 22:57, 21 August 2005 (UTC)

The text says

The illustration below shows the first few iterations in the construction process.

but the illustrations have disappeared (OrphanBot deleted them because they were unsourced). If the single existing image is adequate, then this text should be fixed. If we want to show the steps in its construction, then the images should be restored and released into PD. --171.64.71.123 23:49, 14 July 2006 (UTC)

HEY! The Sierpinsky carpet has zero area. So, if points of plane which belong to the carpet are black, and the plane itself is white, then the most accurate image of Sierpinsky carpet is the white picture. Sierpinsky carpet is invisible! 188.123.243.103 (talk) 15:46, 2 May 2010 (UTC)

Menger sponge

Not mentioned here is the 3-d analog of the Carpet, the Sponge. However, it was discovered not by Sierpinski but by Karl Menger. I'm not sure if the Carpet was discovered by Menger. Does anyone have more info? David 19:48 Nov 20, 2002 (UTC)

According to a quick web search, Sierpinski proved certain features of the Sierpinski Carpet in 1916 (when Menger would have been 14); Menger published his paper about the Sponge in 1926. Chas zzz brown 01:44 Nov 21, 2002 (UTC)

Thanks! David 21:26 Nov 21, 2002 (UTC)

Copyright

How can a simple graph of a mathematical mapping be copyrighted? That seems unreasonable to me. David 17:46 Apr 24, 2003 (UTC)

HTML approach

For an HTML approach of approximating a Sierpinski carpet, see dive into mark.

I'm sure the intention was clever, but it's pretty hard to figure out as it stands. What is this monstrosity supposed to demonstrate? I'm leaving the link here in case some kind of explanation is forthcoming.
—Herbee 17:42, August 21, 2005 (UTC)

Way back then there was a snippet of JavaScript that created a Sierpinski Carpet using the Chaos game, worked in any modern browser that supported the canvas element. I'm not sure why it was removed? The Java code that is here now is less clear and will only work for those people who have/know about Java compilers.. Mspreij (talk) 22:18, 2 August 2010 (UTC)

java not pasteable

Why have java code if it isn't pasteable into Eclipse such that it will produce a running app? OK, call me a java lamer, but I can't get it to run. Either updated code, or a pointer to how to get the samples working would be appreciated. --Markhu 03:11, 24 August 2006 (UTC)

For anybody interested, in Eclipse you can run this right away by putting it in a new java file and running it as an Applet (hit Shift+Alt+X with the file open, then hit A). 69.3.185.246 01:51, 19 February 2007 (UTC)

Remember to enclose in a for loop iterating over x and y, and implement some drawing code. On another note,

x -= x2 * width / 3; y -= y2 * height / 3; should be replaced with x%=width/3+1; y%=width/3+1; . I would also change the base case to if(width<=1) 68.144.80.168 (talk) 02:00, 4 April 2011 (UTC)

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 03:39, 6 January 2007 (UTC)

See Talk:Sierpinski number. I haven't examined "Sierpinski carpet". PrimeHunter —Preceding undated comment added 12:11, 6 January 2007 (UTC)

needs info or link on antennas

I watched a nova that featured fractals a while back, and I could swear that the cellphone antennae was a seirpinski carpet. If this antenna design is common for cellphones, then a note should be made on this page. 68.144.80.168 (talk) 01:41, 4 April 2011 (UTC)

Error in comment?

One of the code comments reads "if in the centre square, it should be filled." I believe the comment should read "empty," not "filled." —Preceding unsigned comment added by 74.94.138.81 (talk) 13:41, 16 May 2011 (UTC)

Stupid Java Code

The code on the page is slow, complicated, and difficult to understand. The following is much simpler, and is in fact the fastest possible code to generate the fractal by iteration. Feel free to comment it and move it to the main page.

   boolean fill(int x,int y)
   {
       while(x>0&&y>0)
       {
           if(x%3==1&&y%3==1)
               return false;
           x/=3;
           y/=3;
       }
       return true;
   }

One of the most basic mistakes with this fractal is to think the filling of pixels is dependent on the size of the piece which due to the nature of being a fractal is insignificant. A 27x27 will be the same as the top left (or any other depending on how you view it) corner of at 81x81 or any larger one Jnaruk (talk) 03:06, 25 December 2011 (UTC)

Universal curve?

Right now the article says:

The carpet is a generalization of the Cantor set to two dimensions (another is Cantor dust). Sierpiński demonstrated that this fractal is a universal curve, in that it has topological dimension one, and every other compact metric space of topological dimension 1 is homeomorphic to some subset of it.

I'm pretty sure this is false. First, the trefoil knot, or any other knot, is not homeomorphic to any subset of the Sierpinski carpet. Second, over on the Wikipedia page for Menger sponge, it's claimed that the Menger sponge is the universal curve. The mere fact that Menger sponge is a curve (a compact metric space of topological dimension 1) is another way to see that the Sierpinski carpet is not the universal curve, since there's obviously no way to find the Menger sponge as a subspace of the Sierpinski carpet - while there obviously is a way to do the reverse.

So, I'm going to fix this and maybe try to add a reference for the actual correct statement, namely that the Sierpinski carpet is universal among curves that are subspaces of the plane.

John Baez (talk) 02:46, 29 June 2014 (UTC)