How do I randomize a motion graphic?

I created a ripple motion graphic using a vector shape that was primarily done with the transform tool and roughen edges effect.

For the taper effect, I changed the values inside the roughen edges panel to create some distortion along the edges. Here is a similar method to the one I used in this video: Water Ripple Motion Graphics | After Effects Tutorial - YouTube

I'm trying to figure out how I would go about seamlessly randomizing the tapering/distortion effect per loop cycle.