Using Cymatics and standing waves of sound to make 3d shapes Goto page 1, 2  Next
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ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Fri Jul 19, 2013 8:22 pm    Post subject: Using Cymatics and standing waves of sound to make 3d shapes Hi all... Cymatics is a fun part of physics and acoustics that studies patterns of standing waves that happen when vibrating objects like water and metal plates are shaken at one frequency. anyway here is some demos: http://pinterest.com/janfufu/lightsound-waves-cymatics/ there is a ted lecture on that page with alot of pics. It's very complicated maths, because, if you vibrate a round 2d circle of metal for example like a drum, waves will bounce from the edges, it will make star patterns, concentric patterns, and all kinds mixed together, until it reaches a kind of balance. abit like the sound of a drum going through different phases. some people have done emulations of them, and they are interesting shapes to apply to the 3 axes of an iso surface. I would like, for example, to emulate wave patterns with complex frequencies that exist in circles and triangles and squares, and to multiply them across axes into 3d shapes. probably because i dont understand how to how to rationalise how the patterns echo back to themselves and stabilise over time.
Furan

Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

 Posted: Sat Jul 20, 2013 10:39 pm    Post subject: Several weeks ago I tried to compute it with FEM software that I'm taking part in developing. Visualy its really boring. However I plan to connect it with my renderer and than hopefully some cool images will emerge. So stay tuned
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Tue Jul 23, 2013 2:16 am    Post subject: That's very amazing! in terms of difficulty and clear result it's the best. it's a very difficult topic in the study of sound. I would be tempted to see it as a kind of 2d raycasting analogue, where the rays bounce all through the shape being vibrated, and devide into wavelength, till they find the most stable zones of the wavelength in a reflection from all borders. that said, i dont think the sound even reflects from the edges of the plate... hmm here is the best emulation i could find: http://universallyaware.ning.com/forum/topics/cymatic-tonoscope-software-finally-available-the-best-universal-l
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Thu Aug 08, 2013 1:20 pm    Post subject: i found this page about it, some explanation of chaldni algorithms for 2d and 3d: http://paulbourke.net/geometry/chladni/
Furan

Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

 Posted: Thu Aug 08, 2013 3:05 pm    Post subject: That is amazing, I was curious how would 3d wave nodes look like. Hopefuly this year I will calculate some of them in more complex bodies and visualize them. There is actually a very nice field of scientific research in wave mechanics: The Resonant Ultrasound Spectroscopy (present also at my institute), which determines material properties from spectral characteristics. I mean, how cool is that? https://www.google.com/search?q=resonant+ultrasound+spectroscopy&client=firefox-a&hs=dqn&rls=org.mozilla:en-US:official&channel=fflb&tbm=isch&tbo=u&source=univ&sa=X&ei=E7IDUs-ZO43HsgbWlYGABg&ved=0CDgQsAQ&biw=1158&bih=713
Furan

Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

Posted: Thu Aug 08, 2013 4:38 pm    Post subject:

Just finished this. I added noise to get the realistic feel of this sorts of experiements. Oops, I may have over done it with the salt

 Code: u = [0.5 0.5]' - rand(2,1); u = u/norm(u)/2; v = rand; U = u(1)*x-u(2)*y + v; f = cos(N*pi*x/L)*cos(M*pi*y/L)-cos(M*pi*x/L)*cos(N*pi*y/L); f = 1.3/(1+(5.25+4.75*sin(U))*100*f*f)-rand/2; RGB(i,j,1) = f; RGB(i,j,2) = f; RGB(i,j,3) = f;
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Sun Aug 11, 2013 9:01 am    Post subject: Hi there, that's extraordinary!. I would love to see some notes on the code, i can't say that i understand it at all! (N,M,L vars? radomisation process?). the patterns are very interesting because they truly seem to correspond to vibrations modes of a metal plate. On the same day also, i attempted to emulate reflections of water drops backwards to a centre from 4 straight edges of a square. here is the result: http://www.youtube.com/watch?v=cUgHNWGjlcQ&t=2m50s less good video: https://www.youtube.com/watch?v=sVteR9TEYF8 i prefer the multiple symmetry of the code you have written, it's very interesting.Last edited by ufoace on Mon Aug 12, 2013 2:20 am; edited 2 times in total
Furan

Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

 Posted: Sun Aug 11, 2013 10:10 am    Post subject: "The less good video" was much better I assume you switched the links. u is a random vector in xy plane. rand = 0..1 rand(2,1) creates random [0..1,0..1] U is just a large wave simulating the initial sprinkle of salt. Initial f is just the wave form according to the Chladni solution Then I'm using function 1/(1+x^2) on it, which is similar to Gauss curve to pick the zero value (node) of the wave function. 5.25 and 4.75 adjusts the effect of the sprinkler wave, 1.3 and 100 adjusts the power and width of the white lines. rand/2 creates the sandy look.
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Mon Aug 12, 2013 6:23 pm    Post subject: Is it a programming language like CG? why are there thre RGB values i,j,1 to i,j,3? i almost understand now
Furan

Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

 Posted: Mon Aug 12, 2013 6:37 pm    Post subject: RGB is the image array, i-th row, j-th column, 3 color components. It's actualy Matlab.
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Mon Aug 12, 2013 6:49 pm    Post subject: N and M are for the polar coordinates?
Furan

Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

Posted: Mon Aug 12, 2013 7:12 pm    Post subject:

N and M are wave numbers according to the Chladni theory, see the page above. In the animation I use N,M = 1..15, from vectors like these:

 Code: M = [2 3 3 4 4 4 5 5 5 5 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15]; N = [1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8  1  2  3  4  5  6  7  8  9  1  2  3  4  5  6  7  8  9 10  1  2  3  4  5  6  7  8  9 10 11  1  2  3  4  5  6  7  8  9 10 11 12  1  2  3  4  5  6  7  8  9 10 11 12 13  1  2  3  4  5  6  7  8  9 10 11 12 13 14];

to cover all possibilities.
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Mon Aug 12, 2013 9:19 pm    Post subject: Oh Sorry i Forgot to read the Paul Bourke formula, i just passed it and it didnt correspond to language that i know to describe maths so i figured i had to study it later!!! Anyways... I've noticed that it presents some similarities with the mandelbox formula. it's similar to folding many circles and many squares together. The emulator i did just folds 100'ds of concentric circles into a square geometry, and it is similar to chaldni and to mandelbox patterns, except that mandelbox is 3d. so it brings to the question... perhaps there is a 2d mandelbox equivalent... hm i will have to ask over at the fractal forus website
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Mon Aug 12, 2013 9:23 pm    Post subject: if ever there was a time to mention morbus cyclometricus :]
ufoace

Joined: 11 Mar 2013
Posts: 46

 Posted: Sun Aug 18, 2013 7:13 am    Post subject: i wrote a program to see if there could be a practical use for the cymatics for precedural generation. it's abit crazy: https://dl.dropboxusercontent.com/u/114667999/Public.html
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