Making Relicated objects appear more random

Here's what I've got:
A circle shape, fill turned off and outline turned on and thickened, brush type changed to airbrush, opacity of brush altered to have a light middle surrounded by dark front and trailing off to a dark back, and Rate behavior used to rotate the Z axis - so basically is looks like a ghosted stroke rotating in a circle. No problems creating that.
When I use the Replicator to replicate the shape, I get a whole bunch of the same circle - which is exactly what I want - but all of the circles are moving in unison. When one stroke is in the 12 o'clock position, all strokes are in the 12 o'clock position. I'm try to get a little variety in there.
Is there a way to have each of the different replicated rotating cicles be at a different point in their rotation so they are not all at the exact same point in their rotation at the same moment in time?

I'm not so much worried about about varying the speed of each circle (I do understand your recommendation that I would need different circles with different rate behaviors for that), I'm just wanting to get each circle at a different point in its rotation. I will try Mark's recommendation.
Come to think of it, though, I am going to hit another problem with this project. After I get the circle rotating at the speed I like, I'm going to want to offset all of the other circles in their rotation (using Mark's recommendation) but then rotate each circle individually to almost 90 degrees but keep it a 2D layer.
(Mr. Neil, I am trying my hand at doing a Star Trekky transporter effect. I know we discussed this a while ago and you provided a link to what you did. I am seeing if I can get something similar)

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    Message was edited by: wideEyedPupil

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