Hello Emil,
A few things spring to mind when looking at that animation:
The background dots – these could be made like this:
Create a shape layer
Add a path going from one side of the screen to the other
Add a dashed line
Add a gap to the dashed line
Adjust the dashes/gaps, and keyframe those values
Add a repeater to repeat in the y-axis all down the screen
The circular smeary lines: There’s a plugin on aescripts.com called Thicc Stroke. I’ve never used it, but it’s free, and I think it can do stuff like this.
Background lines going diagonally: See above – same as the other bg dots. If I was doing it, I’d create a separate shape layer for this, and just carefully line it up with the ‘straight’ bg dots.
0:26 – nothing of interest happens here. The image merely slides off screen (position x keyframes) and fades out, with motion blur turned on.
Tapered dash to centre – could be that Thicc Stroke plugin. Else it could be done (tediously) with repeated shape layers, with the scale set to, say 95% for each repetition. Or it could be done by animating the squares moving from the outside to the centre, then using the Echo effect to show lots of frames ion screen at once.
Experiment and enjoy!
~ Paul