In Illustrator you can apply a Transform effect that allows you to scale, rotate, move an object and create copies.
With it, you can make patterns like this:
I want to have animation control over the different properties, so just importing from Illustrator won't help me.
Is there an effect inside AE that I'm missing? How about a plugin or script that can do something similar?
This can be done with Shape Layers using the repeater function on position location and anchor point
If you were good at trigonometry you could write an expression that would do this on a regular footage layers.