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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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 Posted: Sun Aug 18, 2013 8:14 am Post subject: |
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It's gorgeous !!! What types of wave functions are you using?
Platni pattern, radial and circular wave forms? Anything else?
I will create some animations like this for http://furan.sweb.cz/MathPainter.htm
I wonder if this could be done in 3D. With no blobs or bubbles, more like a stem-like gyroid, changing smoothly. |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Sun Aug 18, 2013 11:53 am Post subject: |
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Thankyou, i was amazed by the variety of shapes that the formula made. it would be nice if it could display different types of patterns, the only thing i can think of for further variations is use it as a base from which geometric procedural forms can be arranged.
The equation consists of at least 5 concentric sinus waves. One in the middle and 2 on each axis. as if one wave exists in the middle and 4 bounce back from each side of a square pond. with these 5 sines, it looked very amazing, so i added 4 more to see what happens when the waves bounce back from either end, i wanted make cymatics:) the waves are added together 1+2+3+4+5...
The variations in the pattern comes from changing the distance of the 4 axis sinuses from the centre to the same distance, changing their amplitude and period using the same values for all 4.
I was aware that the sines would have very complex interactions at the diagonals and in the corners, so i added also a concentric polar rose to the centre that can have 2-4-8 symmetries... by making a very varied wave in the centre, it can amplify many combinations of the surrounding 4 waves into the same image.
to make it 3d is straightfwards, just arrange 1 central spherical sine and 6/12 sines around the axes and add them together. |
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Furan
Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic
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| Posted: Sun Aug 18, 2013 1:27 pm Post subject: |
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Thank you for the info.
For 3d this would make islands and bubbles. But what if instead of adding we used multiplication. That could work. I'll try that. |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Sun Aug 18, 2013 8:38 pm Post subject: |
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| very nice animations also! an interesting page is that of Flexi23, he programs and collects all kinds of mamethatical models. |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Wed Aug 21, 2013 2:26 pm Post subject: |
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I just did a fast test of the wave convergence program using triangle waves instead of sin wave, acos(sin(x)) is triangle.
The iso shapes are interesting for isosurfaces, as they are pointy, although i think that would translate to ridges in 3d, i would prefer spikey objects with spirals  .
here is a video:
http://youtu.be/WaS0OCFe5NA |
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ufoace
Joined: 11 Mar 2013
Posts: 46
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| Posted: Tue Aug 27, 2013 2:38 pm Post subject: |
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I tried some 3d work based on this stuff, i think i should place the sines on a ramp to focus them at the centre.
Hihi! i like these graphis programs, i had an artefact 
http://www.youtube.com/watch?v=KRX5xAet7fw |
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