Recursion

Of course. We already have a method to draw a star, so just use it. The new stars need to be smaller than the central star. So the size of the new stars is size/3. (Other sizes will also work. You may wish to play with this.)

 
  // Grievously Awful Method
  //
  private void drawStar( int x, int y, int size )
  {
    int endX, endY ;
     
    // Six lines radiating from (x,y)
    for ( int i = 0; i<6; i++ )
    {
      endX = x + (int)(size*Math.cos( (2*Math.PI/6)*i ));
      endY = y - (int)(size*Math.sin( (2*Math.PI/6)*i ));
      graph.drawLine( x, y, endX, endY );
      drawStar( endX, endY, size/3 ) ;
    }
  }

The basic star method is easily modified by inserting a statement that puts a star on the end of each line.