Translate/To Circle
 
 

The Circle translation maps the texture to a circle around its center. The x-axis is translated to the angle, the y-axis to the radius.

You can make the texture map itself multiple times around the center by increasing the Tiling values. For instance Image 2 was made with the 3x1 settings. The fractal appearance of Image 3 was achieved by iteratively applying the function to the same texture.
Set a Source Texture to have it mapped to the circle instead of the texture itself.