The graphics controller is in the base of the computer.
The row drivers and column drivers (chips) are on the edges of the display.
Did you drop your computer, spill something on it recently, or something else happen?
It is possible there is a loose cable connection as well between the drivers and graphics controller chip.
I think the macbook air may be using the integrated graphics controller so it is part of the processor.
I suppose there might be a power issue, are you running on battery or AC and is there any difference.
It might be a screen issue as well. Apple has some hardware tests that can be run that might narrow it down. Look for LED screen testing for the macbook.