How to visualize the vorticity of a 3D velocity field? [closed]

I sample a snapshot from a system with 50 particles including their position and instant velocities.

The snapshot is a list of 3 position and 3 velocities values per particle. i.e. 50 lines each of which is comprised of $(x,y,z,\dot{x},\dot{y},\dot{z})$ (AKA phase space coordinates).

My data set's layout is similar to the one used in Making a ListVectorPlot3D from data in an external file, hence it is, basically, a velocity field in 3D.

I want to calculate and plot the following properties of the dynamics: curl, div, stream of the fluid in 3D, vorticity.

How can I visualize those attributes of the velocity field in 3D? Something like this in 3D would be great: I have only a 2D presentation:

In addition I think that calculating and to visualize the Covariance or correlation between the pairwise particles could be interesting too.

data = Import["http://pastebin.com/raw/6Werdnpf"];
vecdata = Partition[#, 3] & /@ DeleteDuplicates[data];
Graphics3D[{ColorData, Arrowheads[Medium], Arrow[{First@#, Total@#}] & /@ vecdata}]
ListVectorPlot[Map[Most, vecdata, {2}]]  closed as too broad by Kuba♦, corey979, m_goldberg, Young, MarcoBFeb 13 '17 at 20:35

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• @C.E. frankly speaking, I am open to hear any suggestion. I want to plot the vortex lines in 3D, the vorticity, the div, or any other CFD property of the velocity field. Or any visualization of the 6D phase space or its subspaces. – 0x90 Feb 5 '17 at 7:44
• ok, it's a legitimate question but if it doesn't receive any answers and you still want something then I would recommend to rewrite it as a question purely about Mathematica, along the lines of "I have this data. I want to make this type of plot. How do I do it in Mathematica?" – C. E. Feb 5 '17 at 8:50
• @C.E. no problem, thank you. I just don't want to limit people's creativity by giving such a reference plot. – 0x90 Feb 5 '17 at 9:00
• Please STOP editing the title to bump up the question on the homepage. This question doesn't need 15 revisions... This question was cross-posted on Stack Overflow as a MATLAB question, which makes me agree with C. E. that this is a physics/I-need-this-done-somehow question masquerading as a Mathematica question. I would be inclined to close it as Off-topic: Out of Scope. – rm -rf Feb 6 '17 at 3:45
• @R.M, It is purely a mathematica question in which I try to plot the vorticity of a vector field. Both this and the SO post are related though by the fact that I am trying to plot the same data set. – 0x90 Feb 6 '17 at 3:52