That depends on what you mean by "swirls".  Basically, you need to think
of the animation as a series of still frames (as in a frame of a movie,
not as in a window).  You need to:

1) Create member variables that store the state of the animation for a
given point in time.  This could be the position at which you are going to
draw something, an image index, parameters that control an
AffineTransform, something else, or a combination of any or all of the
above.

2) Write a method that will modify the state, advancing it to the next
frame.  If the state consists of a position, you might add some offset to
the position, or compute it using some other formula.  Or if using a
series of images, you would probably just increment the image index.
Obviously, this will depend on how you store that state.

3) Figure out how to draw the still frame for any given state.

4) Use a javax.swing.Timer to advance the state on a regular interval, or
possibly an irregular interval.  When the state changes, the component
should repaint() itself, or possibly just the portion of itself affected
by the change.