I wish I knew how to do this.
Award-winning print ad from 2007 for Grassroots in Calgary.

The brush is the ellipse
Using brush to stroke a circular set of paths (set within each other on separate layers), then scale each layer would perform the same results.

Example

I'll give it a go later. I thought about making a brush first.
Isn't there a script to make an expanding spiral pattern? I seem to remember Lyle was playing around with that.

I think he was using MathMap.

Not quite what you wanted. Anyway, created a single over brush and then tiled Horizontally and used theilr's Pan to Bow to create a Circular ring. I then dup/shrunk/rotated the ring. I then ran Mathmap's Droste9 (as a side note, the original Droste9 didn't work for me, but when I downloaded Graechan's files when he shared how to get Mathmap to work with 2.8, his worked and so did many other of the presets that didn't work for me in my version of Mathmap; not sure if Graechan indeed fixed the presets or my install was corrupted when I did them at that time) to create the result. Also, just another excuse to create a wormhole. lol

That's very good Lyle. I thought it was you who was playing with the wormhole stuff.

That is a keen idea Lyle.Using a straight line of brush strokes and then bending them in a semi circle.
Love the way you laid that image out too. Very eye boggling.

Thanks for the comments; can't watch this one for too long since it sort of gives me vertigo. lol

Hey Lyle you created another pretty nice circle of shapes with brush dynamics too.That would be another cool way to do this.

Yes; you can do this and it has to be a path and not a selection (only GIMP 2.7/2.8 of course). The problem is choosing the brush spacing (hit or miss procedure). Theilr's Pan to Bow (makes sure you have transparent spacing half that of the spacing between objects on each side of the horizontal result; also make sure you have transparent spacing below that is 25% larger then the height; should probably have mentioned this before; lol) Script-fu just does is with much better consistency.