As requested on Google+, here are the project SLA and resources (swirl1.zip).
Note that the image used was exported from Page 2 of the document, then it was put back into two different frames on Page 4 which is where the main effect was created.
(I've removed the text and other layers that weren't relevant to the technique.)
The process to get the swirl uses various layer blends, gradient fills and image effects. It's too long to explain and requires a lot of experimentation but you can pick it apart if you look deep enough.
And, just for comparison, swirl2.png/sla shows a similar effect without using any images at all. (It's not quite as good as the original because you need the blur effect to make it look right and that has to come from an image frame.)
I hope these things give some people a bit of inspiration to create some funky effects of their own.
If you use this technique - or something similar - please share it with the community so everyone can see what's possible.