Re: 4D Visualisierung

On 9/15/2024 2:11 AM, guido wugi wrote:

Op 15-9-2024 om 02:17 schreef Chris M. Thomasson:

On 9/14/2024 5:10 PM, Chris M. Thomasson wrote:

On 8/28/2024 12:30 PM, guido wugi wrote:

Hallo,

[...]
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This is your artificial 4d axis, right?
>
https://i.ibb.co/rMqqp9k/image.png

 Exactly. I called them (x,y,z,v) here, but (x,y,u,v) for complex functions. The positions are initiated by the six angle controls for coordinate plane rotations (or four angle controls for "spherical" coordinate rotations).

Okay. I see. Thanks.

To be quite honest, 4d kind of freaks me out a little bit... If 3d is comprised of infinite 2d planes, then 4d is comprised of infinite 3d planes...

 Yes, 3D-manifolds aren't much indicated for visualisation of course.
It's all about *surfaces and edges*:
Pure surfaces and their parameter curves as for complex functions.
Or border edges of border surfaces, of (border) volumes of 4D-volumes, as for the tesseract.
If you want 3D-volumes in 4D, that's another pair of sleeves (as we say in Dutch:-).

Yeah. That's an interesting one for sure. So, a 3d volume would be one 3d plane out of the infinity of them in the 4'th dimension? Humm...
Btw, I have created a lot of 3d volumes. Even in DICOM format. They are all good candidates for holograms... :^)
Check these out if you can get to the link:
https://www.facebook.com/share/p/n2nMhW5G2PhRzyfx
They can all be 3d printed. Humm... Sometimes I think that a 3d "observer" would only be able to see 2d. As in a 3d scene projected onto a 2d plane with lights and shadows, ect... However, a 4d observer would be able to see in pure 3d. Make any sense? Thanks.