How to create a wormhole grid animation

How to create an animation like this? Using Ae or Blender (maybe another program).

I’ve never used Blender and I’ve only played around with After Effects, so I don’t know the steps necessary to recreate this. But it looks pretty simple.

The curved lines leading down into the hole are stationary; they don’t move at all. The ellipses that appear to move down into the hole are a stepped blend between two offset concentric circles. There appears to be a black-to-transparent radial blend in the depths of the hole on a layer above everything, which provides the illusion of the lines disappearing into nothingness deep within the hole as the animation proceeds and loops.

Creating the static curved lines that lead down into the hole appears to be the only difficult part to make look correct. How that was done, I don’t know. For all I know, even that would be simple in a 3d application.