We start with a blank canvas, but we will also define a pattern to use, first. Open a new document 20x20pixels, then paint half of it one color, and the other half another color, like so:
Next, press Ctrl + A to select all, and then goto Edit > Define Pattern and give it a name.
Next, go back to your original document and choose the Paint Bucket tool. From the toolbar at the top, choose Pattern instead of Foreground, then choose the pattern we just created from the dropdown menu to the right:
Then we can fill in our document with this pattern, using the Paint Bucket:
Next, we will add a Filter > Distort > Polar Coordinates, and choose Rectangular to Polar. And there we have it:
You can expermiment with different colors and also different patterns to come up with different outcomes.
More Tutorials: 
