Think of it like this: a gutter is perceptible until it is obstructed (or almost so). This only happens when two successive lines are almost completely out of phase (with the black segments in the first line lying nearly above the white segments in the next). Such extreme situations only happens about one out of every 10 rows, hence the visible gutters which seem to extend around 10 rows before being obstructed.
Looked at another way — if you print out the image, there really are longish white channels through which you can easily draw a line with a pen. Why should your mind not perceive them?
To get better visual randomness, find a way to make successive lines dependent rather than independent in such a way that the almost-out-of-phase behavior appears more often.