How to create this pattern effect

Multiple copies of a shape layer overlapped and used as track mattes will create this kind of thing. Here's your example:

I would start with a couple of shape layer circles and a segmented track matte for the left side then keep animating and duplicating. It's nothing more than layers, and track mattes.

That took me about 3 minutes.

You can try Motion Tile effect (not quiet sure about this), or just create a narrow comp, put the pre-comp of the animation in it, place and time it, create a new narrow comp and repeat. In the end you have several narrow comps with you can align to each other add filters and have this effect - driven by one and the same animation.

There are at least 5 other ways, though.

*Martin