I coincidentally play this video while listening a Philip Glass álbum. It was funny to find out very late that the music video were not coming out of Glass jeje. (Btw, here a big big toroidal fan, i really Love your channel).
Gracias caballero. Not sure if Philip Glass (Koyaanisqatsi!) uses fractal lines in his music. I made this in my youth, before having heard of fractals and before knowing that my "guido's sequence" is actually called Thue-Morse sequence ;o) BTW do you know John Adams and his Harmonium? Also great repetitive music.
I'm interested in the effect of the rotation of 4D objects on the 3D components, specifically the direction of the 4D acceleration vector. Could you demonstrate/investigate? Great video.
I'm not sure what you mean but I'll answer for the best. In 4D the base planes (eg, the X and Y plane, the real and imaginary plane) have a single point intersection: the origin. A rotating base plane does so around its complementary base plane, eg, X rotates around Y, the imaginary plane around the real plane (this is so because it rotates around any direction of the other plane). The acceleration vector points to the intersectioin of the rotating plane and the axis (3D) or plane (4D) of rotation, in our case the intersection of both base planes, ie, the origin. As for the effect of the 4D rotation on 3D components, I understand this as "how is the rotation seen in 3D?". Well, that's exactly what is shown in the video: projections of the rotating 4D object onto 3D or, in our case, onto 2D (a flat screen!) but which can be "re-interpreted" as 3D space. (I notice that I've messed up between axis notations x+iy and z+iw, versus x+iy and u+iv)
Well, it is "true 4D", projected in 3D-style on to 2D screen ;-) The "true 4D" part is correct though, and rather seldom seen, most mainstream math prefers 3D-extractions...
Thanks! Go to my music site www.wugi.be/muziekte.htm and look for "Fraktet". You can download the .mid, .mp3, .pdf score and .encore files. I didn't know at the time I created it (as a youth:-) that the fraktet theme represents actually the en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence . (Hint: you can paste video url links and extract mp3 music here: mp3-youtube.download/en )
This video: ua-cam.com/video/KUwWPsXFLOA/v-deo.html shows, how to create 4D cubinder (4D cube, which built from 3D cylinders). If you want to create your own 4D shapes, you can use the link, which is in description under that video.
Thank you. I'm happy to deal with 4D surfaces, but I'm afraid 4-dimensional 3D-spaces are beyond my capabilities! ;o) Anyway, generally speaking only surfaces can be rendered, even in 4D: 4D volumes and 3D-in-4D volumes can only be rendered by their bordering or generating surfaces, see renderings of tesseract and 3-sphere for example.
The z plane (abscis) is formed by the x and y axes. The w plane (ordinate) by the u and v axes, which incidentally I first called the z and w axes in the video, and then proceeded calling it the u,v plane :o) Basically z=x+iy, and w=u+iv (or w="z"+i"w", sorry for that).
@@wugionyoutube Have you made videos on the duocylinder? I find it very difficult to visualise. And what is a tiger? I heard it is extremely difficult to visualise.
The blanket at 3am when ur trying to find the correct side:
I coincidentally play this video while listening a Philip Glass álbum. It was funny to find out very late that the music video were not coming out of Glass jeje. (Btw, here a big big toroidal fan, i really Love your channel).
Gracias caballero. Not sure if Philip Glass (Koyaanisqatsi!) uses fractal lines in his music. I made this in my youth, before having heard of fractals and before knowing that my "guido's sequence" is actually called Thue-Morse sequence ;o) BTW do you know John Adams and his Harmonium? Also great repetitive music.
I'm interested in the effect of the rotation of 4D objects on the 3D components, specifically the direction of the 4D acceleration vector. Could you demonstrate/investigate? Great video.
I'm not sure what you mean but I'll answer for the best.
In 4D the base planes (eg, the X and Y plane, the real and imaginary plane) have a single point intersection: the origin. A rotating base plane does so around its complementary base plane, eg, X rotates around Y, the imaginary plane around the real plane (this is so because it rotates around any direction of the other plane). The acceleration vector points to the intersectioin of the rotating plane and the axis (3D) or plane (4D) of rotation, in our case the intersection of both base planes, ie, the origin.
As for the effect of the 4D rotation on 3D components, I understand this as "how is the rotation seen in 3D?". Well, that's exactly what is shown in the video: projections of the rotating 4D object onto 3D or, in our case, onto 2D (a flat screen!) but which can be "re-interpreted" as 3D space.
(I notice that I've messed up between axis notations x+iy and z+iw, versus x+iy and u+iv)
BTW thank you.
It looks 2D, 3D and 4D at the same time
Well, it is "true 4D", projected in 3D-style on to 2D screen ;-) The "true 4D" part is correct though, and rather seldom seen, most mainstream math prefers 3D-extractions...
Yes, you are seeing correctly. Each dimension is composed of it's lower dimensions. Randal J. Bishop
Pls upload this music to google drive or similar, I WANT IT!
Thanks! Go to my music site www.wugi.be/muziekte.htm and look for "Fraktet". You can download the .mid, .mp3, .pdf score and .encore files. I didn't know at the time I created it (as a youth:-) that the fraktet theme represents actually the en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence . (Hint: you can paste video url links and extract mp3 music here: mp3-youtube.download/en )
@@wugionyoutube yeah, thanks
Great Work!
Thank you! (have you seen the other video of the C. Torus and its 3D projection combined?)
Guido W.
Yes - and your website - thanks Brother!
I have never heard of a Clifford taurus, but I love them now
Thank you, I appreciate. It's also a rather recent discovery for me (and more so the "taurus", could it be a bull's eye? ;-)
*torus
You are melting my brain
Look for my latest Clifford torus videos, for enlightenment ;-0)
"PERFECT."
Thank you!
makes me feel uneasy to look at it.
Perhaps you don't fancy 4D exploration ;-)
That music
A musical Thue-Morse sequence... "discovered" by meself when a child knowing nothing about fractals...
@@wugionyoutube Interesting videos
This video: ua-cam.com/video/KUwWPsXFLOA/v-deo.html shows, how to create 4D cubinder (4D cube, which built from 3D cylinders). If you want to create your own 4D shapes, you can use the link, which is in description under that video.
❤
I know this is a wild request, but have you ever rotated a Ditorus?
I believe Quantum objects are 4th Spatial-dimension shapes
Thank you. I'm happy to deal with 4D surfaces, but I'm afraid 4-dimensional 3D-spaces are beyond my capabilities! ;o) Anyway, generally speaking only surfaces can be rendered, even in 4D: 4D volumes and 3D-in-4D volumes can only be rendered by their bordering or generating surfaces, see renderings of tesseract and 3-sphere for example.
You forgot the w plane
The z plane (abscis) is formed by the x and y axes. The w plane (ordinate) by the u and v axes, which incidentally I first called the z and w axes in the video, and then proceeded calling it the u,v plane :o) Basically z=x+iy, and w=u+iv (or w="z"+i"w", sorry for that).
I don't understand a thing
Me too. I’m going to research more about it.
It is like how a circle is to a sphere that the taurus is to a Clifford taurus
@@forlorneater6595 Taurus? Wtf is that
In the mean time there are 5 videos ("Wugi's 4D world") dealing with the Clifford torus and its companions.
@@wugionyoutube Have you made videos on the duocylinder? I find it very difficult to visualise. And what is a tiger? I heard it is extremely difficult to visualise.