Hopf Fibration Stereogram (Divergent)
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- เผยแพร่เมื่อ 3 ก.ค. 2014
- This animation is a stereogram, so if you view the left image with your left eye and the right image with your right eye, it should produce the illusion of being 3D. Focusing your eyes properly for this effect can take some practice. If you're unsure how to do this, I would recommend viewing on a small screen (like a smart phone) and start with it very close to your eyes and gradually move it away until it comes into focus.
If you prefer crossing your eyes to view stereograms, visit this link for a convergent version of this video: • Hopf Fibration Stereog...
en.wikipedia.org/wiki/Hopf_fib...
This animation was created by first subdividing the vertices of an icosahedron to generate points on the unit 2-sphere. These points are rotated in 3-dimensional space and then mapped into 4-dimensional space as circles via the Hopf map.
To visualize how points on the 2-sphere correspond to circles under the Hopf map, I recommend this excellent video: • Hopf fibration -- fibe...
These circles are then rotated and then projected back into 3-dimensional space with stereographic projection.
The color is assigned based on the initial spherical coordinates of each point and remains constant throughout the video.
The specific rotations were obtained by generating a (smoothed) random walk on the 9 dimensional manifold RP³×S³×S³, where RP³ corresponds to the possible rotations on the input points (SO(3)), and S³×S³ corresponds to the set of rotations on the output circles (SO(4)).
This was created with F# and Mathematica, and then rendered in Unity 4.5. - วิทยาศาสตร์และเทคโนโลยี
do you understand any of this jaime?
canal canal lol! This is jre reference? 🤞👍👏👏👏❤️😄
@@ashleyandchloe It must be haha, I like Weinstein a lot. cool guy
I don't think I have the tools
This is a stereographic projection of a Sphere of which is embedded in 4D space. All of the fibers you see were originally great circles of the hypersphere before they were projected. Also, these circles do not intersect each other in 4D space. Stereographic projection preserves this property, so once the circles are projected to 3D space, they also don't intersect there.
That was fabulous! Some of the best I've seen.
This is beautiful. Thank you.
This gives me the tingles.
I want an Imax version of this. It's way better than most of the modern movies.
это просто великолепно! я в восторге, спасибо большое)
Excellent work!
Beautiful! 👌
Наверное, для восстановления зрения прекрасное упражнение!!!
Beautiful
Amazing! Practice with this will help me through my next dmt trip thankyou! 🙏
Hey do you have any tips on how to find dmt? I know of a video of how to extract it from Ayahuasca, but I live in an apartment and the chemicals required to do it will leave your place smelling very bad for a day or two. I have had plenty of psilocybin, MDMA, and molly experiences but I'm really trying to find the spirit molecule. Any tips would be greatly appreciated. Thanks!
Wow, so cool. I come to here from tomary. Very cool.
I saw this nearly exact thing my first DMT experience
that is amazing
Very cool👏👏👏👌
What do I have to do to see it properly?
So what can you do with it?
I saw sometimes 4 of those rings and most of the time 3 ist this normal?
2 of the 4 overlap and creae a 3d effect
so yes this is normal
I am looking for someone who can produce a customized hopf fibration view for me. Would you be able suggest how best to source this?
I know how to plot it in mathematica...at least. My skills don't come close to the person who made this video though
Choice!
I like this one because you dont need do do weird xross eye to get it going
Unsolicited advice maybe 4k for better bitrate so get that extra clarity for the intricate parts
What's the music?
Hi, does anyone know what soundtrack this is?
Puddle of Infinity - Hydra 😊
Dear Magical Beings,
I Enjoy this mass of squared light but can't get the stereo effect from my present primitive instruments. It would be most excellent if you could put this and other visualizations on 3-D computer "game."
Most sincerely, Yoda Leahey O
Can someone give the steps to do this?
cool
I'm great with still stereograms, but this one is not working for me. Hard as I look, it's not appearing!
Love this 4D opening into 5D
It's much better with the vr goggles then to watch it so close
I wonder what the golden ratio has to do with this
Holy video compression youtube. I bet this is neat uncompressed.
Double the Hopfs in your Beer if you like which you can have without quality water!
❤️
Probably the closest I'll ever get to having an LSD experience
@Devin G actually it is
@@solefood7477 no it really isn't, this is more similar to intense DMT visuals but even then the comparision isn't great.
Hard but fun
When you guys watch this video, do you prefer watching it as two images or three? I do it both ways
You just go crosseyed and move your head until it makes a weird 3D image in the centre.
Well, unfortunately, for that you need left part of screen for a right eye, and right part of screen for a left one.
In this case it's straight left for left eye and right for right. So you need to straighten your eyes, but screen is too wide for that.
Dreams of a Bladerunner.
i put another stereogram side to side and i could see a three dot but not in this video
FYI it took me only 5-10 secs to see every stereogram pict then this one took me 5 minutes still no clue
if u concentrate hard enough, you'll see a man rotating down and up the stairs.
I see what you are saying.................sort of
Whoever said it's cats'' pictures that internet is for was wrong. This is what internet is for.
See Ken Wheeler on magnetism.
I am here father. I am not lost.
Unfortunately it was too "busy" at some points, so it refocused my eyes again at some points
Yeah, when it was zooming out with the things appearing from behind especially
Tomary?
Ich
Weißt du wie man das scharf sehen kann ? Ob man das scharf sehen kann ?
Das mache ich immer unbewusst
1:02 this moment threw me out of focus
Yeah but post Korean war - the North modernized first and also provided food assistance to the south. The north did not close off entirely and both sides had continued interest in unification. This video glosses over all nuance to sell you the idea that Capitalism is the key to everything. A feel good story.
Joe rogan got me here
lost when it went really close
That guy on Rogan was full of shit. Spinners? GTFO? I've read a few books on QM and never ehard of them, google 'spinners QM' and you'll get nothing.
Look please very nice animation of big magic squares on torus for big numbers - such homepage under number-galaxy eu.