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 |