Look at the background in a Roman figure mosaic and your eye will naturally follow the way the lines of tesserae have been set. Sometimes the lines will be horizontal over the whole of the background area, often though you will see that the lines are horizontal in some areas, vertical in others and diagonal over other parts.
Why is this?
Simple, it just depends on how the mosaicists were sitting. When you set lines of tesserae it is normal to set them going right to left (if you're right handed) in lines that are horizontal to you. You can set more tesserae hat way than going vertically before having to move your position.
Now if you have more than one person working on the floor, as you would have had, then they may be facing a different way to you. They set their lines horizontal to the way they are sitting but this may then mean that their lines are vertical or diagonal to yours. Where the lines meet they just blend them together.
One way to judge the standard of an ancient mosaic is to look at the background areas and the better ones will have all their background lines on one lie, usually horizontal. The images shows how different lines can be set, the drawings represent a birds eye view of the mosaicists.