Visualization of Riemann Surfaces
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- čas přidán 9. 01. 2011
- This animation depicts a disk of the complex plane as it is acted upon by a range of polynomial equations.
For the most part, f(z) = z*(z^k - 1) for k=1 to 6.
A blend of three different functions is used to control the height coordinate.
Spherical shapes are generated using stereographic projection.
I wrote custom scripts to model and animate the geometry.
For presentation I used a dielectric glass material and a 'final gather' lighting setup. - Věda a technologie
Beautiful. Great job. Wonderful how the branch cuts, poles and zeros come into view. At times the surfaces appear to breathe.
I use Maya for rendering and animation. I wrote custom scripts to manipulate the geometry.
oh wow, this video is soo old. thanks for still replying to the comments. tip: u can pin this comment :)
I watched a 30 minute presentation on the complex loci of z=w^2 and how in the compactification of the complex plane, it is topologically a sphere. I didn't understand as much as I wanted to but the visual aids in that look like the figures here.
¡What a beautiful visualization! Thanks for uploading this!
Really beautiful!
Lovely animation - thank you for this!
Exquisite!
@rjravaz Believe me, as someone who studies this stuff, no good explanation, not even a mediocre one via metaphors would fit in this boxes. Takes semesters of study to understand this stuff. I am not saying you wouldn't understand it, just saying that its unrealistic to pretend to explain it in a couple of paragraphs.
Is this kind of like a hopf fibration?
fantastic and to think it was done 9 years ago!!!
11 years and counting!
what program did you use for the visualization?
He used Maya. You can use Blender instead, as that is a FREE open source software.
Where in this is the Y-Axis?
this is imprortant
Good ol' friend number i
Can you explain to me where this relates to anything in life or math? Thank you.
the real world is actually described by the riemann geometry, which is the mathematical foundation of einsten's general relativity. so, yes,this is the world that we're living in, but it's impossible to vizualize.
@@derivativecovariant2341
Can you prove it ?
@@derivativecovariant2341 riemann surfaces are not a part of reimannnain geometry
Recently, I have been able to resolve Riemann's Z Function and Prime Numbers with the Partitions Theory. I wrote 2 equations that are linked by the Length module of Prime Numbers. With these equations can I analyze real and imaginary plane. For these Solution I have created news concepts to make awesome Solutions. I have got all the trivial and no trivial zeros for both planes. Partition theory is capable to analyze Periodic and No Periodic Functions without limitation in Period, or Angular Speed.
You can see these two videos for the solutions to Prime Numbers and RIemann's Z Function.
czcams.com/video/Lk3n2cQpiF0/video.html
czcams.com/video/QieWM4IlNmM/video.html
Cool, but next to meaningless without explanation or context
Even with the explanation I wouldn't get it
Umm... you know he included a description, albeit generally in prose? If this video didn't stimulate your thinking on these surfaces, what else motivated you to click on this?
3d bugs cant understand 4d giant