My favorite part of the article:

>From what I can tell, one of the settings used to deal with division by 0 is the so-called Riemann sphere, which is where we take a space shuttle and use it to fly over and drop a cow on top of a biodome, and then have the cow indiscriminately fire laser beams at the grass inside and around the biodome. That's my intuitive understanding of it anyway.

also:

>Our cow isn't staring into infinity. It's looking down at infinity, observing infinity with detached understanding. If our cow were not so enlightened, and also had the facial muscles, it might betray the subtlest of smiles at infinity's infinity face, for infinity's turbid fractal whirlpools and vast lethargic swamps are but swathes of data like any other to this cow.

What may not be obvious without (or, actually, even with) reading the actual article is that that stuff about cows on biodomes actually is a (rather facetious) way of describing what the Riemann sphere is.

Also:

> You might be wondering why we don't just ask a biologist about these mysteries. The reason is because you're inside a car right now, I'm driving, we're lost, both of us are tourists, and I'm one of those people that would sooner burn hours of gasoline/diesel than ask for directions. You also suspect I might be some kind of criminal, so you're afraid of bringing up the issue. All around it's pretty awkward in here.

The page as a whole does seem a little like it charts a descent in to a holey, triangular insanity.

One of the coolest parts of the article is at the very end when he algorithmically constructs music with the sierpinski triangle. http://www.oftenpaper.net/img/sierzrp1.mp3

I was blown away by the observer/house sketch. Philosophically speaking, I'm glad you guys are here.

Aww, platonically speaking we're glad you're here too :)

Previous thread : https://news.ycombinator.com/item?id=6516114

should get more upvotes to be seen

This is certainly more detailed than mine but I also have a blog post (http://lifebeyondfife.com/87-beauty-html/) documenting three different methods and the JavaScript code to make these in an HTML5 canvas on GitHub: https://github.com/lifebeyondfife/Sierpinski.

EDIT: After going back for a further look, saying that the original link is more detailed than mine doesn't do justice to the amount of content (images, animations, code, explanations) there actually is.

If you like this kind of stuff you might also like this:

http://obadger.com/turtle/

Then paste/run this program:

    var triangle = (function(){
      function frag(len, depth, left){
        if (left === undefined) left = !(depth % 2);
        if (depth > 1) {
          frag(len/2, depth-1, !left);
          t[left?'lt':'rt'](60);
          frag(len/2, depth-1, left);
          t[left?'lt':'rt'](60);
          frag(len/2, depth-1, !left);
        } else {
          t.fd(len);
        }
      }
      return frag;
    })();

    /* position the turtle */
    t.pu().bk(250).rt(90).bk(350).pd().color('#0f0');

    /* build the triangle */
    triangle(700, 8);

Wow - I don't think I'll sleep tonight. I want to reprogram all of this myself. Thanks for sharing!

I first saw this when I happened to be struggling with the early Project Euler problems. The deeper insights and analysis it offered, combined with the sense of humour, really helped me understand and solve the simple problems where a straightforward "Intro to X Concept" failed.

For some good hands-on intuition of the Sierpinski Triangle check out this tutorial on using some open-source (research) software to build a tile-set which will self-assemble the Sierpinski triangle: http://self-assembly.net/wiki/index.php?title=Sierpinski_tri...

Last summer I received an undergraduate research grant to work on ISU TAS (the above linked software). So I'd love to see more people using it outside of the research community!

For more information on algorithmic self-assembly in general http://self-assembly.net

For the depth and length of this article, I'm pretty surprised he didn't seem to mention the Sierpinski triangle patterns that can occur on shells, see: http://www.gmilburn.ca/2009/07/16/i-see-sierpinski-shapes-by...

There was a time I was impressed by a program that drew the sierpinski triangle.

The executable file was 31 bytes: http://osix.net/modules/article/?id=756

> There's a good chance that subgraph is hideous because it contains one of the 3 end vertices of the graph as a whole, though I'm too lazy to check this.

Too lazy to check that? Somehow I highly doubt it!!! haha

I once wrote a tetrahedron sierpinski gasket... Was very fun, but always made my then GeForce 3 graphics card overheat at about 10 or 11 sub divisions.

At first I thought the title was link-bait, but it isn't much of an exaggeration. The topic is explored deeply.

wow... well that's taken up most of my workday and ruined my time for side-projects at the same time. Brilliant article.

I could only think of the triforce the whole time.