Re: 4D Visualisierung

On 9/14/2024 2:08 AM, guido wugi wrote:

Op 13-9-2024 om 23:58 schreef Chris M. Thomasson:

On 9/11/2024 1:22 PM, guido wugi wrote:

Op 11-9-2024 om 10:15 schreef Chris M. Thomasson:

On 9/11/2024 1:12 AM, Chris M. Thomasson wrote:

On 8/28/2024 12:30 PM, guido wugi wrote:
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Check this out:
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https://youtu.be/IVR5I5mnrsg
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;^)

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Also, iirc, this experiment of mine has a vector with a non-zero 4d component...
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https://youtu.be/KRkKZj9s3wk

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I don't understand it, but they're beautiful graphics alright! But 4D?
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Meanwhile I've put a Desmos4D graph of Clifford tori, Dupin cyclides (also shown together!) and Hopf fibration.
bolnorm4D.CT-DC-HF | Desmos <https://www.desmos.com/3d/rwj9vo31yc?lang=nl>
https://www.youtube.com/watch?v=1y6qrsJff-g&list=PL5xDSSE1qfb6c7UHcURl6wXh0pH4ARB75&index=21
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Here is an example of a 4d vector ping ponging through -1...1 wrt its w component:
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https://www.facebook.com/share/v/PC17LfU94uUjW6DY
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So, the single attractor is at point (0, 0, 0, w) for the animation. There is a major effect on the field. Here is another simulation that shows the attractor at a fixed (0, 0, 0, 0) for the entire duration:
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https://www.facebook.com/share/v/DXKhRoGZmpB9fX5Y/

 I don't see really the difference, sorry.

There is a massive difference. Humm... The animation is rather fast. Try it in slow motion.

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?

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).
Humm... I need to work on another animation that shows this off more, clearly...