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Author Topic: Sierpinski triangle  (Read 4887 times)
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Buddhi
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« on: November 22, 2009, 09:28:43 PM »

Few days ago I found on Internet some pictures of Sierpinski Triangle and Sierpinski Temple (David Makin's pictures). It is very beautiful mathematical form. Unfortunately I didn't find any detailed algorithm. I decided to found proper algorithm by myself. I made lots of trials and before I understood how this kind of iterative algorithms works I get some interesting pictures. One of these is below.   


http://www.fractalforums.com/gallery/?sa=view;id=1088

Finally I found proper algorithm and rendered this "Sierpinski's Planet"


http://www.fractalforums.com/gallery/1/640_22_11_09_9_01_17.jpg

Bellow is my iteration algorithm in C
Code:
double k=2.0;
double a_off = 0;
double b_off = 0;
for (L = 0; L < N; L++)
{
  xx = fmod(a * k+a_off, 2.0);
  yy = fmod(b * k+b_off, 2.0);
  zz = fmod(c * k, 2.0);

  if ((zz>1.0)&&(xx<0.5 || xx>1.5 || yy<0.5 || yy>1.5))
  {
result = 0;
break;
  }
  k *= 2.0;
  result = 1;
  if(zz>1.0)
  {
     a_off = 1.0;
     b_off = 1.0;
  }
  else
  {
     a_off = 0;
     b_off = 0;
  }
}
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Dinkydau
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« Reply #1 on: November 25, 2009, 02:57:05 PM »

The second one is really cool!
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Timeroot
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Posts: 362


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« Reply #2 on: February 04, 2010, 07:11:37 AM »

It took me a while to realize these were square pyramids, not the regular sierpinksi pyramids. This means that, although there does seem to be a "floor" in this picture, the "floor" is dense, and it could extend onwards who-knows-how-far... a very simple, yet awe-inspiring image. Reminds me of the ancient Aztecs.  grin
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
kram1032
Fractal Senior
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Posts: 1863


« Reply #3 on: February 04, 2010, 11:44:44 AM »

due to them being cubes, you could actually build them... I wonder how stable they would be smiley
(Not using any glue between the cubes)
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Timeroot
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Posts: 362


The pwnge.


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« Reply #4 on: February 04, 2010, 05:30:23 PM »

Yes, but you would have to build it upside down - note that many of the edges of the "floors" aren't supported by anything. By inverting it, we could get a buildable structure.... but it would tip over pretty easily. Would make an interesting problem for civil engineers, that's for sure!!!!
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
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