Sujet : Re: 4D Visualisierung
De : chris.m.thomasson.1 (at) *nospam* gmail.com (Chris M. Thomasson)
Groupes : sci.mathDate : 15. Sep 2024, 00:46:50
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vc579a$1o4dp$1@dont-email.me>
References : 1 2 3 4 5 6 7 8
User-Agent : Mozilla Thunderbird
On 9/14/2024 2:41 PM, guido wugi wrote:
Op 14-9-2024 om 21:20 schreef Chris M. Thomasson:
On 9/14/2024 2:08 AM, guido wugi wrote:
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I don't see really the difference, sorry.
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There is a massive difference. Humm... The animation is rather fast. Try it in slow motion.
The thing is, it doesn't expose dim 4. It looks and feels like just an external parameter acting on the output.
No. Its an integral part of the vector field. If I did create an artificial axis in 3d and say okay, that's the 4d axis... Then I would be able to plot points like (-1, .1, -.4, 2). Right now I am only plotting the 3d components. The 4d field makes some very strange field lines. Here is one where a strong attractor is in the 4'th dimension. The field lines want to go off into a spiral like formation. Strange to me:
https://www.facebook.com/share/p/RqFqkaeLxQhN7UkSAnother one using different colors so its a little bit easier to see in a sense:
https://www.facebook.com/share/v/H6jeFAV1TprPyyaRPutting an attractor in the 4'th dimension causes some very strange effects on the field. It almost makes the field lines wants to spiral into a tube and go off in another direction. Keep in mind that I can only see what the 4d does to the 3d lines. I can't actually plot a 4d point.
Humm... Perhaps I will experiment with creating an "artificial axis" in 3d to place 4d points on. So, (0, 0, 0, -1) and (0, 0, 0, 1) would both be on that artificial axis. Humm... interesting.
And: where is the w component *in* the graph? If it isn't *in* the graph, it's just some external parameter upon a 3D-graph, isn't it?
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Well, the vector field algorithm is working on 4d vectors. However, I don't know where to plot a vector like (0, 0, 0, 1) unless I define some other axis in 3d. This does not seem quite "kosher" to me. Anyway, I can only see what the non-zero w components do to a field that has all zero w's. The 4d definitely casts an influence on the 3d components (x, y, z).
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Humm... I need to work on another animation that shows this off more, clearly...
It's precisely what my thread is about.
*Graphing 4 dimensions in 3D, spherical-symmetry-true.*
You might try it out with your app ;-)
Well, humm... You know, I just might give it a go. However, I am a bit busy right now with a pretty neat collision avoidance thing using my field algorithm. Some examples:
https://www.facebook.com/share/v/rf2AQAFmivdtJxkf/https://www.facebook.com/share/v/VRv48n97MRoMPxwn/Well, the fun part is that my 4d fields generates points that are actually 4d and plotting them on an artificial axis might be interesting. Humm... Each axis would have a different color, so we can see whats going on. Humm...
Mainstream math apps ought to try it out. But they prefer going on happily ignoring 4D possibilities. Except for tesseracts, for some reason.
It's nice work. Thanks for sharing it. :^)
thanks.