Apologies for the lack of clarity. I neglected to mention that after swapping the rows I also reordered the columns so that they were in ascending order of the bitwise representation of their stars. So before:

  . . . x * * * (row 2, bit value 4) 
  . . . * * * * (row 1, bit value 2)
  . * * . . . * (row 0, bit value 1)

  0 1 1 2 6 6 7 (bitwise column values)
[download]

after swapping rows 0 and 1:

  . . . x * * * (still row 2)
  . * * . . . * (was row 0, now row 1)
  . . . * * * * (was row 1, now row 0)

  0 2 2 1 5 5 7 (new bitwise column values)
[download]

and after reordering columns:

  . x . . * * *
  . . * * . . *
  . * . . * * *

  0 1 2 2 5 5 7 (new bitwise column values)
[download]

Similarly the second swap gives columns (0, 1, 4, 4, 3, 3, 7), and reordering the columns gives (0, 1, 3, 3, 4, 4, 7).

Does that make it any clearer?

Hugo