[kevinwang]

Hm, I'm not knowledgeable about this subject but this seems like the offset on each row is NOT random, but it's instead repeating. Imagine instead that each time I added a new row, I chose the offset to be, say, a completely new value.

[irishsultan]

Doesn't matter, because your new row will still be offset with the same random value to existing rows after moving one square to the left or right.