March 24, 2010
http://www.aes.org/e-lib/browse.cfm?elib=5755
I have been communicating with Adrian Freed at the Center For New Music and Audio Technologies at UC Berkley about our research. He pointed me to the paper linked above
links for Adrian Freed:
CNMAT website: http://cnmat.berkeley.edu/people/adrian_freed
blog: http://cnmat.berkeley.edu/user/adrian_freed/blog
May 6, 2009
Manipulate[
where = PolyhedronData["Tetrahedron"][[1, 1]];
tet = PolyhedronData["Tetrahedron"][[1]];
oct = PolyhedronData["Octahedron"][[1]];
octn = {RGBColor[0.6, 1, 0.2],
Rotate[oct, ArcTan[Sqrt[2]], {0, 1, 0}]};
octn2 = Scale[octn, 2 {1, 1, 1}, {0, 0, 0}];
d2 = Map[Translate[{tet}, #] &, a where];
d3 = Map[Translate[{octn, d2}, #] &, b 2 where];
Graphics3D[{d3, octn2}, Boxed -> False, SphericalRegion -> True,
ViewPoint -> {-5, 20, 5}, ViewAngle -> Pi/60],
{{b, 1, “divide tetrahedron b”}, 0, 2},
{{a, 1, “divide tetrahedron a”}, 0, 2}, TrackedSymbols -> {b, a}]
April 27, 2009
Here is the Mathematica code modeling of 2D vibrations of the rectangular region excited by a sine function.
k[x_, y_] = Sin[x + y]
Sin[x + y]
a[n_, m_] =
4 / (l1 l2) Integrate[
Integrate[
k[x, y] Sin[n Pi x / l1] Sin[m Pi y / l2], {x, 0, l1}], {y, 0, l2}]
-(4 (-2 n \[Pi] Cos[2] Sin[m \[Pi]] +
n \[Pi] Cos[n \[Pi]] (m \[Pi] Sin[4] + 2 Cos[6] Sin[m \[Pi]]) -
4 m \[Pi] Cos[4] Sin[n \[Pi]] +
8 Sin[6] Sin[m \[Pi]] Sin[n \[Pi]] +
m \[Pi] Cos[
m \[Pi]] (n \[Pi] Sin[2] – n \[Pi] Cos[n \[Pi]] Sin[6] +
4 Cos[6] Sin[n \[Pi]])))/((-4 + m^2 \[Pi]^2) (-16 +
n^2 \[Pi]^2))
Manipulate[
Plot3D[Sum[
Sum[a[n, m] Cos[
c Sqrt[((n Pi x / l1)^2) + ((m Pi y / l2)^2)] t] Sin[
n Pi x / l1] Sin[m Pi y / l2], {n, 1, B}], {m, 1, M}], {x, 0,
10}, {y, 0, 15}, PlotRange -> {-10, 10}]
,
{t, 0, 10},
{B, 1, 10},
{M, 1, 10},
{l1, Exp[-25], 12},
{l2, Exp[-25], 10},
{c, 0, 5}
]
April 24, 2009
So I had an idea after some coffee and reading through Sapoval’s article as well as a bunch of related stuff. Can we possibly guide the light, or electromagnetic wave in general, in the direction we need using some 3D structure, for now not necessarily a fractal, or alter the waveform in some other way? That is basically what we are shooting for, but I just browsed through general info on density of states, which led me to photonic crystalls, and so I was thinking about applying the related principle to our project’s light part. As I understand it, highly ordered structure of photonic crystalls together with the principles of diffraction, energy levels, and DOS allow, say, opal crystalls to work the way they do: cancel some wavelength of light, enhance other ones, giving us that pretty blinkage (couldn’t find a better word, pardon my English:). My question is then, since according to the property of scale invariance of the electromagnetic fields, and hence waves, does it make any sense to assume that certain fractal structure we are yet to construct/find/copy would cancel out, say, wavelength in the microwave range could be applicable to reducing noise in antennas maybe, or if we create the structure small enough to work with visible light wavelengths, could we possibly get some artistic effects out of the cancellation/enhancement effects of the structure? This is just a flow of thought I did not want to lose in the morning, so it is quite disordered. The basic idea would be, I guess, could we apply principles of photonic crystall structure to the analysis and maybe construction of fractally shaped wave cancellation setup, or maybe wave altering setup?
Links:
April 23, 2009
April 21, 2009
April 21, 2009
April 17, 2009
Tyler converted Sapoval’s Fractal Drum into a 2D SketchUp file. After some trial and error, he figured out the pattern and made the image on the right through repetative additive process of the smallest component. The file on the left was exported for use with a CNC machine.
February 24, 2009
Processing- good, simple, and pretty programming environment based on java for generating fractals and modeling some behaviors
Pure Data- excellent tool for sound synthesis and data analysis. Can also be used for 2D and 3D visual modeling.
eMotion- a combination of tools that I usually build in Processing and the interface is sort of similar to the Soda Constructor (only available for Mac 10.5)
http://www.adrienm.net/emotion/eMotion.html
February 22, 2009
According to Dr. Peterson and Stas, the area that the sound needs to hit to bounce predictably and not just disperse randoming would be approximately one half meter (0.5 m) wide and tall. If we made the height of the interior triangle 50cm that would make the sides 58cm and the area of the triangle 1450 square cm (1/2 * base * height). The question I have is, if this is our minimum dimensions for predictable results, won’t all of the other smaller triangles in the structure be irrelevant because they will just randomly disperse the sound? or are we hoping that they will do something predictable since they are in the fractal pattern?
