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ufoace
Joined: 11 Mar 2013
Posts: 46
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 Posted: Fri Jul 19, 2013 8:22 pm Post subject: Using Cymatics and standing waves of sound to make 3d shapes |
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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. |
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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| Posted: Sat Jul 20, 2013 10:39 pm Post subject: |
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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 
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Tue Jul 23, 2013 2:16 am Post subject: |
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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 |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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| Posted: Thu Aug 08, 2013 4:38 pm Post subject: |
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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;
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Sun Aug 11, 2013 9:01 am Post subject: |
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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 |
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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| Posted: Sun Aug 11, 2013 10:10 am Post subject: |
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"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. |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Mon Aug 12, 2013 6:23 pm Post subject: |
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Is it a programming language like CG? why are there thre RGB values i,j,1 to i,j,3?
i almost understand now |
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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| Posted: Mon Aug 12, 2013 6:37 pm Post subject: |
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RGB is the image array, i-th row, j-th column, 3 color components.
It's actualy Matlab. |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Mon Aug 12, 2013 6:49 pm Post subject: |
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| N and M are for the polar coordinates? |
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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| Posted: Mon Aug 12, 2013 7:12 pm Post subject: |
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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. |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Mon Aug 12, 2013 9:19 pm Post subject: |
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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 |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Mon Aug 12, 2013 9:23 pm Post subject: |
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| if ever there was a time to mention morbus cyclometricus :] |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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