Why is it called 4D?

[WAS]

4D indicates a 4-dimensional euclidean space, and space-time is not supposed to be confused with this physical dimension. So why is it called 4D for time based stuff in 3D programming? When the 1D, 2D, 3D all refers to euclidean space, and thus ana and kata movement of objects?

I've tried to search for the origins of the terminology for 3D software stuff but can't find anything.

PS I realize it does translate to movement in most software that I know of like Terragen's 4D noise, but it's also referred to as time for the movement or what not which confuses me from all explanations which explicitly tell you not to confuse with time-space, which is what these programs seem to be referring to, like TG.

Is this why there is no vector based movement of velocity, and it just being frame by frame "time" or however that may be explained?

[Kadri]

4D indicates a 4-dimensional euclidean space, and space-time is not supposed to be confused with this physical dimension. So why is it called 4D for time based stuff in 3D programming? When the 1D, 2D, 3D all refers to euclidean space, and thus ana and kata movement of objects?
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Not sure i understand you correctly. But the first 2 sentences looks like it says different then your question?
"In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. The fabric of space-time is a conceptual model combining the three dimensions of space with the fourth dimension of time."
https://en.wikipedia.org/wiki/Spacetime

If you work for an image you are working in 3d. If you work for an animation (+ time) it becomes 4d.
Not sure what you are asking specifically Jordan.

[Kadri]

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PS I realize it does translate to movement in most software that I know of like Terragen's 4D noise, but it's also referred to as time for the movement or what not which confuses me from all explanations which explicitly tell you not to confuse with time-space, which is what these programs seem to be referring to, like TG....

Curious...Where?

[Kadri]

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Is this why there is no vector based movement of velocity, and it just being frame by frame "time" or however that may be explained?

I am not much into mathematics you know. But some other software does have much more control over animation.
There are most probably more options for movement, velocity etc.

And even in Terragen when you play with TCB or linear settings you are using actually those (velocity etc.) in a limited way.

[WAS]

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PS I realize it does translate to movement in most software that I know of like Terragen's 4D noise, but it's also referred to as time for the movement or what not which confuses me from all explanations which explicitly tell you not to confuse with time-space, which is what these programs seem to be referring to, like TG....

Curious...Where?

On the power fractal page, and the fact it only works based on the timeline like blender and other stuff.

https://planetside.co.uk/wiki/index.php?title=Cloud_Fractal_Shader_v3

4D indicates a 4-dimensional euclidean space, and space-time is not supposed to be confused with this physical dimension. So why is it called 4D for time based stuff in 3D programming? When the 1D, 2D, 3D all refers to euclidean space, and thus ana and kata movement of objects?
...

Not sure i understand you correctly. But the first 2 sentences looks like it says different then your question?
"In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. The fabric of space-time is a conceptual model combining the three dimensions of space with the fourth dimension of time."
https://en.wikipedia.org/wiki/Spacetime

Yes, and compare to https://en.wikipedia.org/wiki/Four-dimensional_space which is based on 4 dimensions of space, where the 4th is more akin with velocity. Ana and Kata.

Here is a topic I read earlier in a facebook discussion about this: https://www.infobloom.com/what-is-the-fourth-dimension.htm
Quoting the first paragraph which is a good quick summary of the 4th dimension of space.

The fourth dimension is generally understood to refer to a hypothetical fourth spatial dimension, added on to the standard three dimensions. It should not be confused with the view of space-time, which adds a fourth dimension of time to the universe. The space in which this dimension exists is referred to as 4-dimensional Euclidean space.

[Kadri]

As an example in ligthwave this is only one small tab for motion of particles. There are more options on other tabs.
And Lightwave does have much more deep controls that i haven't used at all even.
More modern apps like Houdini are probably even better at this.

[Kadri]

Do you mean this:

"4D noise Click this checkbox to enable 4D noise. 4D noise is always different from 3D noise, so expect deformations to change when this setting is enabled." ?

Not sure but i think this is trying just to say that your noise pattern will be different when you click this. Nothing more so far i know. Or nothing more deep at least .

[Kadri]

The other space dimension parts are needlessly confusing i think.
If you think about string theory for example there are 10 and more dimensions.

If you ask me (you shouldn't ) All those theoretical dimensions are just that. Kinda abstract mathematical games.
I have my own thoughts about this but that is another thing.

[WAS]

Not sure but i think this is trying just to say that your noise pattern will be different when you click this. Nothing more so far i know. Or nothing more deep at least .

Read the second, where you select speed, and this is all based on the timeline, or frame. And is just an XYZ position. Same for moving around objects, no velocity like you show with Lightwave. Which I think is why we can't have blurred objects by the frame based on velocity and the camera.

[WAS]

Well the 4th dimension of 3D space is pretty concrete. Otherwise, nothing would quite work. Everything would be stationary. It's the mathematical extension of 3D space which gives us as previously mentioned the 4th axis, ana/kata. This is like setting up a vector velocity for an object, probably similar to what you showed in Lightwave. Least this is my understanding. But Terragen and I think I've seen it mentioned in other software 4D being time based, with the timeline and frames.

This may be a good topic which I am starting to read now: https://fleischfilm.com/animating-the-4th-dimension/

But in summary I am wondering why it's called "4D" when 4D is supposed to represent 4 dimensional space, not space-time, and in TG it seems to be a relation between space-time and evolution of noise?

[Kadri]

Wait i will try a basic render to show something. Not sure if it will help.

[WAS]

Also what I mean with objects is like objects in TG when you animate them, they just exist at a location in every frame, they don't have a vector through 4D space. They use space-time to translate [as the key]. ()

[Kadri]

You don't need vector for this...so to speak.
Think as an baked fbx animation that you get from another software for those particles for example.
Every place that object is is one frame-keyframe. You might have used momemtum, different velocity etc in that software.
But in the end that object is going from one point to another one in time. When you bake this in a FBX file you get the same result.
So you could do the same frame for frame manually for every object in Terragen too basically...hard to do of course.

Anyway hard for me to say what i want...
But you are kinda making it more complicated then it is if you ask me.
Every motion (velocity, momentum or whatnot...) is just a place-keyframe baked-sliced in 3 dimension basically.

[WAS]

Every motion (velocity, momentum or whatnot...) is just a place-keyframe backed-sliced in 3 dimension basically.

Well, the point of velocity is based in physics. That's how you can get a still of motion blur with that data. Things just existing at a location don't allow that. They're just there, no data for speed, trajectory, and in some simulations instances, weight influence with gravity.

This video is pretty cool: https://www.youtube.com/watch?v=4TI1onWI_IM and I guess the PF is a 4D "object" or noise. So I guess it is 4D after-all and like you said was thinking too much into as I was also thinking about objects and velocities (I was having a discussion on blender fluid sims and wishing we had particles)

[WAS]

Those videos also make the CInema 4D hyper-this and hyper-that makes a little more sense, and why you could do crazy warping and explosions with them.