Aright, this is one I should have done a while ago since it's so simple, and produces some cool effects.
This tutorial we'll be working with the Distort > Polar Coordinates filter. That is essentially all it is doing, however there are some things to realise. All photoshop filters are based upon math (formulas, algorithms) and the Polar Coordinates one is one of the ones which is most susceptible to Placement.
Placement is really only a factor with filters which take the canvas, and the objects therein into effect. Polar Coordinates is one of these. You can do the filter once, undo it, move your element and do it again and the result will be completely different. Millimeters make a difference!
I'm not saying this to stress you out, but to tell you to PLAY with this little tool, have fun. I used to do abstract pieces of art based solely on 1 shape with a Polar Coordinates. People would always see something different in them. It's not a tool you'd use for photo manipulation (though it can be funny do have fun with your boss's face), but it can be useful.
Aright, here we go, our target is something like the background here:
http://server2.tacf.org/examples/borg.jpg (large file)
1. Make a new image
2. Make lines like this:
http://server2.tacf.org/examples/lines.jpg
3. Filter > Distort > Polar Coordinates > Rectangular to Polar
Now, you'll want to try rotating the lines, moving them around, changing the number/thickness/spacing of them, etc. Essentially have fun!
TECHNIQUES: Circly Circles 
Linear Mode
