Randomize Repeater Trim Paths
I'm trying to create an animated "radiating light" using only trim paths in AfterEffects. I'm aiming for a flat, single-color, line-art style (see the Illustrator sketch below):

Currently, in AfterEffects, I have a single line animated with trim paths. I then used a repeater and rotated it to make it a radiating animation. This works great if I want each instance of the line to be exactly syncronized with the original, but I want each instance of the repeater to animate randomly so that it looks similar to the sketch in illustrator. Is there a way to do this?
Here's a screenshot of what it currently looks like in AE:

Any input on this would be great! Thank you!
