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Community => Let's collaborate on something! => Topic started by: Bent-Winged Angel on September 01, 2010, 02:25:48 PM




Title: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on September 01, 2010, 02:25:48 PM
I have recently become fascinated with them.  Really interested in seeing what others would do with them.


Title: Re: SIERPINSKI TRANGLES
Post by: Lorenzo on September 01, 2010, 03:00:21 PM
I also love the Sierpinski fractal construct.  Here's a few of the one's I've created in the past few years: http://www.flickr.com/search/?q=sierpinski&w=32286042%40N00&z=e (http://www.flickr.com/search/?q=sierpinski&w=32286042%40N00&z=e). Regards,  Manny


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on September 01, 2010, 03:07:34 PM
Thanks so much Lorenzo! Gave me some great ideas!  I have just tipped on the iceburg.  Soo New to this.  Also interested in process.  Always stayed away from math.  lol  What programs?  Do you write your own?  I just found them on Chaspro.  Took out a few shears etc. hear & there. Added a swirl or something.


Title: Re: SIERPINSKI TRANGLES
Post by: Sockratease on September 01, 2010, 11:30:25 PM
Fun with Mandelbulb 3D

(http://www.sockrateaze.com/stuff/bnr.jpg)

Huge version - http://www.sockrateaze.com/stuff/bnr.png (http://www.sockrateaze.com/stuff/bnr.png)


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on September 03, 2010, 06:20:26 PM
Socko you made that with mandelbulb?  How annoying are you  :evil1: I trying to figure out sierpinskies with chaospro. Also trying to see the limitations I have with that program. Any advice is welcome.  BTW what's the difference between a sponge, menger?


Title: Re: SIERPINSKI TRANGLES
Post by: Sockratease on September 03, 2010, 08:03:47 PM
Socko you made that with mandelbulb?  How annoying are you  :evil1:

Thanks   :embarrass:

I'm actually Far more annoying in person.  That's why Lissa keeps me caged.  At least I get a computer in here.

I know there's a better explanation, but very basically - Menger stuff is squares, while Sierpinski stuff is triangles.

Now we can await a more expert explanation...


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on September 03, 2010, 08:15:54 PM
Then a sierpinski menger is triangles that make  a square.  Sponge?


Title: Re: SIERPINSKI TRANGLES
Post by: FractalFoundation on September 03, 2010, 08:16:37 PM
Wow I love Sierpinski Triangles too!
Here in New Mexico we started a program to teach school children how to draw them, and then we combine their little triangles into ever larger triangles. Last March, we built the world's largest one, a 6th order version, made of 2187 triangles. Most were made in NM, but many came from all over, including over 200 from Australia.
(http://fractalfoundation.org/wp-content/uploads/2010/03/tthon-1.jpg)

Here's a timelapse video of the assembling of the giant triangle:
http://www.youtube.com/watch?v=6BabkJYmBCA&feature=player_embedded

Here's a few more pix: http://fractalfoundation.org/2010/03/fractal-trianglethon-a-giant-success/
And if any of you want to participate and teach children to make them and contribute to the next, even larger one,  the lesson plan is available here:
http://fractalfoundation.org/resources/fractivities/sierpinski-triangle/
The one you see here is 96' on a side. We have over 4000 already, so we're well on our way to breaking our own record, with the next one that will have 6561 triangles and be 192' on a side...
Fun!!!

Thanks,


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on September 03, 2010, 08:20:13 PM
That is a great way to learn!  I noticed that some of mine look like quilt pieces.


Title: Re: SIERPINSKI TRANGLES
Post by: kram1032 on September 03, 2010, 10:18:59 PM
there actually is a variant that mixes squares with triangles :)

It's like a roof: On the ends, it's two equilateral triangles, on the sides, it's two squares. - that's the menger sierp ;)


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on September 08, 2010, 01:35:20 PM
This is interesting..  http://local.wasp.uwa.edu.au/~pbourke/fractals/gasket/

Now I'm starting to work with ifs system.. putting the pieces together like a puzzle or quilt.


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on September 19, 2010, 05:39:52 PM
I think I've finally learned how to think "inside the box"  I've always tended to do things backwards! :embarrass:  Also thanks to bib for encouraging me to try Mandelbulb3d.  That program made things much easier than I thought they would be. 


Title: Re: SIERPINSKI TRANGLES
Post by: kek on October 18, 2010, 03:25:40 PM
Everybody had an sierpinski fractal antenna in their mobile phone.

http://www.scienceprog.com/fractal-antenna-constructions/

(http://hireme.geek.nz/fractal3.jpg)
http://hireme.geek.nz/ATSC-8VSB-fractal-antenna.html


Title: Re: SIERPINSKI TRANGLES
Post by: chenchen21621 on November 04, 2010, 10:44:52 AM
Here in New Mexico we started a program to teach school children how to draw them, and then we combine their little triangles into ever larger triangles.
 :o :embarrass: :embarrass: :embarrass:


(http://images.icanhascheezburger.com/completestore/2009/2/1/128779945225614728.jpg)


MODERATOR EDIT :  It's nice that you contributed to the discussion, but I removed your spam link for watches!  Please do not use this forum in that manner unless you arrange a proper link exchange and get permission First!  Thanks.


Title: Re: SIERPINSKI TRANGLES
Post by: Thunderwave on November 04, 2010, 10:32:46 PM
I one that was using Menger and it came out as Triangles,
Here's the image I rendered:
(http://www.fractalforums.com/gallery/4/2367_03_11_10_8_14_27.jpeg)


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on November 15, 2010, 02:03:25 PM
Did this a while ago with Chaospro

(http://nocache-nocookies.digitalgott.com/gallery/3/1953_01_09_10_10_16_57.jpeg)


Title: Re: SIERPINSKI TRANGLES
Post by: Wel lEnTaoed on November 15, 2010, 06:17:37 PM
Pretty cool all that can be done with a triangle!

(http://nocache-nocookies.digitalgott.com/gallery/3/2391_23_09_10_10_56_51_0.jpeg)


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on November 17, 2010, 10:27:53 PM
Soemthing went soo, soo very wrong!

http://www.youtube.com/my_videos_edit?ns=1&video_id=h-Y8OI6Tw9Q&next=%2Fmy_videos


Title: Re: SIERPINSKI TRANGLES
Post by: Bent-Winged Angel on November 18, 2010, 10:30:32 PM
Seriously anyone got a clue as to why it crumbled?


Title: Re: SIERPINSKI TRANGLES
Post by: public_v0id on April 23, 2011, 03:31:51 AM
I have recently become fascinated with them.  Really interested in seeing what others would do with them.

Recently stumbled on a connection between the Sirpinski Triangle and the Towers of Hanoi Game:
http://www.youtube.com/watch?v=w_3hCjE6FWU


Title: Re: SIERPINSKI TRANGLES
Post by: PhillyWilliams on September 14, 2011, 04:06:46 PM
There's also a connection between Sierpinski triangles and Pascal's triangle: if you take Pascal's triangle and make it mod 2 (so every odd number is a 1 and every even a 0), you'll end up with Sierpinski's triangle!

Not fun for the artsy crowd, but a cool connection in pure math....

I have a student today who asked me if we could prove that Pascal's triangle is/generates Sierpinski's, but I'll start up another thread for that....


Title: Re: SIERPINSKI TRANGLES
Post by: matsoljare on September 15, 2011, 11:30:04 PM
Yeah, but what happens when you use another number?


Title: Re: SIERPINSKI TRANGLES
Post by: fractower on September 16, 2011, 01:43:15 AM
It turns out mod of a prime number produces Sierpinski Triangles with extra structure in the triangle. Non-primes do produce self similar results but don't include a Sierpinski.


mod2
001          1                                                                                                               
001         1 1                                                                                                               
002        1   1                                                                                                             
003       1 1 1 1                                                                                                             
004      1       1                                                                                                           
005     1 1     1 1                                                                                                           
006    1   1   1   1                                                                                                         
007   1 1 1 1 1 1 1 1                                                                                                         
008  1               1                                                                                                       
009 1 1             1 1 

mod3
001                              1                           
001                             1 1                             
002                            1 2 1                         
003                           1     1                           
004                          1 1   1 1                       
005                         1 2 1 1 2 1                         
006                        1     2     1                     
007                       1 1   2 2   1 1                       
008                      1 2 1 2 1 2 1 2 1                   
009                     1                 1                     
010                    1 1               1 1                 
011                   1 2 1             1 2 1                   
012                  1     1           1     1               
013                 1 1   1 1         1 1   1 1                 
014                1 2 1 1 2 1       1 2 1 1 2 1             
015               1     2     1     1     2     1               
016              1 1   2 2   1 1   1 1   2 2   1 1           
017             1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1             
018            1                 2                 1         
019           1 1               2 2               1 1           
020          1 2 1             2 1 2             1 2 1       
021         1     1           2     2           1     1         
022        1 1   1 1         2 2   2 2         1 1   1 1     
023       1 2 1 1 2 1       2 1 2 2 1 2       1 2 1 1 2 1       
024      1     2     1     2     1     2     1     2     1   
025     1 1   2 2   1 1   2 2   1 1   2 2   1 1   2 2   1 1     
026    1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 
027   1                                                     1

mod4
001                                  1                               
001                                 1 1                                 
002                                1 2 1                             
003                               1 3 3 1                               
004                              1   2   1                           
005                             1 1 2 2 1 1                             
006                            1 2 3   3 2 1                         
007                           1 3 1 3 3 1 3 1                           
008                          1       2       1                       
009                         1 1     2 2     1 1                         
010                        1 2 1   2   2   1 2 1                     
011                       1 3 3 1 2 2 2 2 1 3 3 1                       
012                      1   2   3       3   2   1                   
013                     1 1 2 2 3 3     3 3 2 2 1 1                     
014                    1 2 3   1 2 3   3 2 1   3 2 1                 
015                   1 3 1 3 1 3 1 3 3 1 3 1 3 1 3 1                   
016                  1               2               1               
017                 1 1             2 2             1 1                 
018                1 2 1           2   2           1 2 1             
019               1 3 3 1         2 2 2 2         1 3 3 1               
020              1   2   1       2       2       1   2   1           
021             1 1 2 2 1 1     2 2     2 2     1 1 2 2 1 1             
022            1 2 3   3 2 1   2   2   2   2   1 2 3   3 2 1         
023           1 3 1 3 3 1 3 1 2 2 2 2 2 2 2 2 1 3 1 3 3 1 3 1           
024          1       2       3               3       2       1       
025         1 1     2 2     3 3             3 3     2 2     1 1         
026        1 2 1   2   2   3 2 3           3 2 3   2   2   1 2 1     
027       1 3 3 1 2 2 2 2 3 1 1 3         3 1 1 3 2 2 2 2 1 3 3 1       
028      1   2   3       1   2   3       3   2   1       3   2   1   
029     1 1 2 2 3 3     1 1 2 2 3 3     3 3 2 2 1 1     3 3 2 2 1 1     
030    1 2 3   1 2 3   1 2 3   1 2 3   3 2 1   3 2 1   3 2 1   3 2 1 
031   1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1   
032  1                               2                               1