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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: 4D Visualisierung
Date: Sat, 14 Sep 2024 12:20:12 -0700
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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:
>>>>> [...]
>>>>>
>>>>> Check this out:
>>>>>
>>>>> https://youtu.be/IVR5I5mnrsg
>>>>>
>>>>> ;^)
>>>>
>>>> Also, iirc, this experiment of mine has a vector with a non-zero 4d 
>>>> component...
>>>>
>>>> https://youtu.be/KRkKZj9s3wk
>>>
>>> I don't understand it, but they're beautiful graphics alright! But 4D?
>>>
>>> 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
>>>
>>
>> Here is an example of a 4d vector ping ponging through -1...1 wrt its 
>> w component:
>>
>> https://www.facebook.com/share/v/PC17LfU94uUjW6DY
>>
>> 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:
>>
>> 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...