Let’s consider a simple example.  Suppose we want to cluster black and white intensities, and we have the intensities: 1 3 8 11.  Suppose we start with centers c1 = 7 and c2=10.  We assign 1, 3, 8 to c1, 11 to c2.  Then we update c1 = (1+3+8)/3 = 4, c2 = 11.  Then we assign 1,3 to c1 and 8 and 11 to c2.  Then we update c1 = 2, c2 = 9 ½.  Then the algorithm has converged.  No assignments change, so the centers don’t change.