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If creating a vector field based on an equation is not possible, how create an equation-free 3-D vector field in blender?

The arrows should have color based on the magnitude of force they exert on objects. It would be great if the Vector field, can actually exert forces.

I understand that it's not possible to list everything in a single answer, but if someone can guide me in the right direction, it would be highly helpful.

Something like this

If creating a vector field based on an equation is not possible, how create an equation-free 3-D vector field in blender?

The arrows should have color based on the magnitude of force they exert on objects. It would be great if the Vector field, can actually exert forces.

I understand that it's not possible to list everything in a single answer, but if someone can guide me in the right direction, it would be highly helpful.

Something like this

EDIT: Someone has actually done this, I precisely want to do something like this. https://www.reddit.com/r/blender/comments/8aqyns/vector_field/?utm_source=share&utm_medium=web2x

First of all, how to create an equation-free 3-D vector field in blender? I understand that it's not possible to list everything in a single answer, but if someone can guide me in the right direction, it would be highly helpful.

Something like this

If creating a vector field based on an equation is not possible, how create an equation-free 3-D vector field in blender?

The arrows should have color based on the magnitude of force they exert on objects. It would be great if the Vector field, can actually exert forces.

I understand that it's not possible to list everything in a single answer, but if someone can guide me in the right direction, it would be highly helpful.

Something like this