I had the same problem on my early 2011 15" Macbook Pro
I solved it by resetting the SMC
Reset the System Management Controller to Fix the Striped Display on Boot
This will dump and reset settings for anything power management related, and is long known to resolve problems with things like fans, heat, sleeping problems, and of course, display issues.
On any modern MacBook Pro or MacBook Air with a built-in battery, which is just a bout all of them nowadays, this is how you do that:
Shut down the Mac and connect it to your MagSafe adapter and a wall outlet as usual
Hold down the Shift+Control+Option+Power button at the same time for a few seconds
Release all keys at the same time, then boot the Mac as usual