POLAR COORDINATES

The Polar Coordinates filter works by remapping the geometry of an image. You get two options: Rectangular to Polar and Polar to Rectangular. Rectangular coordinates are like a square piece of paper, while Polar coordinates are life half a sphere. If you want concentric cirlces, this is the filter for the job. Start by drawing a couple of horizontal lines like this:

Run the filter on the image, setting it to Rectangular to Polar. Boom! Instant circles from straight lines. It helps if you hold down your shift key while you draw the lines, this way they join up porperly and are made perfectly straight.

Now start over, but this time draw your lines vertically. Run the filter once more and you get radially converging lines. Not quite useful, yet a fun effect to play around with. You can get interesting results if you paint in different coordinate spaces and use the filter to flit between them.