Re: 4D Visualisierung

On 8/29/2024 3:01 PM, guido wugi wrote:

Op 29-8-2024 om 20:47 schreef Chris M. Thomasson:

On 8/29/2024 7:56 AM, guido wugi wrote:

Op 29-8-2024 om 00:31 schreef FromTheRafters:

guido wugi explained :

Op 28-8-2024 om 21:49 schreef Chris M. Thomasson:

On 8/28/2024 12:38 PM, Chris M. Thomasson wrote:

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

Hallo,

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Actually, it's impossible to visualize a true tesseract in 3d space?
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A question I have is where do I plot a 4d point, say:
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(0, 0, 0, 1)
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in a 3d space? Humm...

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How do you plot a photo of a 3D scene?

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Oh, now you're projecting. :)
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Sorry, couldn't help myself. In another group they all think that they are psychologists.

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Most "3D" renderings of math objects are done in 2D, whether on paper or on screen.
As for surfaces and curves, which is what we do, there is no difference in rendering 3D or 4D ones. The main problem is having a coherent coordinate projection base (conserving spherical rotation symmetry). Which I've had to resolve the last couple of weeks :)
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I don't think you can truly project a _true_ 4d object into a 3d space. We can get some insights, but the projection does not really represent the 100% true 4d object... It does not capture all of the information? Actually, this kid did an interesting explanation, well at least to me: :^)
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https://youtu.be/eGguwYPC32I
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What do you think?

 I find it obvious that we can project from 4D space into 3D space in the same way that we can, and do (everytime you look at a photograph;), project 3D into 2D. What we can't do really, is project 3D-volumes/manifolds. But projecting surfaces and curves works just fine.
 Of course the projected image isn't the "real [4D] thing". But then a photograph isn't the real 3D world it depicts either. Still we like looking at and interpreting photographs/pictures and find them interesting. So how for heaven's sake could one not find 4D-to-3D projected images equally interesting, I ask you???
 So then, my renderings aren't "true 4D" objects alright, but they are "true 4D" projections.

Fair enough. It just seems that to create another axis in 3d space and say its 4d is not quite right. But, then again wrt my fields, I can have attractors in 4d space with non-zero 4d components, and I can only see what they do to the field as its rendered.

Just as the ubiquitous pictures of the Tesseract are already.
But contrary to the usual 3D extractions of complex functions, like Re(w), Im(w) etc, which are effectively cutting off a 4th dimension.
 

Are you familiar with the triplex numbers? How about using quaternions to get 4d projections from Julia sets? This is a nice one:
https://youtu.be/AK9uc9ByruU
I need to find my anaglyphic glasses! :^)