Literal attractor points?

Is there a way to make attractor points that actually attract nearby objects and cause them to move?

Not directly, you have to build that logic yourself. Set up a vector from each object to your attractor, modify the length of that vector through some equation, then move your object along the modified vector.

If you want to have also the simulation of the movement you can use Kangaroo 2.
There you use length goal to reduce the distance between your attractor point and others.

Here’s an example of how you can do it. (11.4 KB)

If you want move the objects manually you can do like this

I’m unable to download the file.