What is a common word for horizontal and vertical lines/directions? I would like to differentiate between vertical and horizontal lines/directions in a dot pattern from diagonal lines. However, I am lacking the vocabulary for it. For instance, here I would like to differentiate between the blue arrows and the black arrows. Is there any term/word for this?

 A: It is very customary to look at a picture such as yours, and to immediately establish two distinguished perpendicular directions. Perhaps not coincidentally, the most popular distinguished directions are the ones in your picture that are painted black.
Since you are interested in words, I point out that your black horizontal axis is traditionally known as the axis of abscissas. Your black vertical axis is traditionally known as the axis of ordinates.
You have drawn your blue directions as bisecting the Cartesian coordinate axes in black. But upon inspection of the definition of diagonal, we find that any direction not one of the four black directions can legitimately be called diagonal. So, I propose that "diagonal direction" is one way to describe your blue directions.
Also worth considering is "skewed direction".
As an example, consider measure theory. It is standard to consider only rectangles "with sides parallel to the coordinate axes". A rectangle along your blue directions does not satisfy this requirement.
