Sierpinski triangle

Buddhi

Fractal Iambus

Posts: 895

Sierpinski triangle

« 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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My fractal gallery: http://krzysztofmarczak.deviantart.com
fractal animations: http://www.youtube.com/user/xlace
Mandelbulber program: https://github.com/buddhi1980/mandelbulber2

Dinkydau

Fractal Senior

Posts: 1616

Re: Sierpinski triangle

« Reply #1 on: November 25, 2009, 02:57:05 PM »

The second one is really cool!


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My gallery: http://dinkydauset.deviantart.com/gallery/

Timeroot

Fractal Fertilizer

Posts: 362

The pwnge.

Re: Sierpinski triangle

« 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

Posts: 1863

Re: Sierpinski triangle

« 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

(Not using any glue between the cubes)


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Timeroot

Fractal Fertilizer

Posts: 362

The pwnge.

Re: Sierpinski triangle

« 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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it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval, thanks and see you perhaps in 10 years again

The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again