There's really no way to preferentially differentiate between the image being flipped one way or the other once the one pixel wide columns have been shuffled. T

There's really no way to preferentially differentiate between the image being flipped one way or the other once the one pixel wide columns have been shuffled. The order of the first pair that you put together determines which orientation you end up with and this is totally arbitrary. The reason that it flips sometimes is because the shuffling of the columns is random and the order of the initial pair of seed columns depends on their original order in the shuffled image.