If you can boot to recovery holding Command + R and see if the issue recurs.
If it does it needs a hardware repair. If it does not try booting to safe mode holding Shift key.
Also Standard SMC / NVRAM resets.
For SMC plugin power adapter
Hold down left hand side Shift Ctrl and Option keys. Push down power button and hold all keys for a couple secs then let go of all at same time. Machine Should not turn on.
NVRAM reset is done by holding Command + Option + P + R while system is booting up. Keep holding til you hear the startup time a second time.
Do the SMC and NVRAM then boot to recovery. If issue recurs you need a hardware repair.
Also if you have AppleCare on the machine, call them and get the issue documented while under warranty. That'll make it so that if the issue happens early outside the warranty they have a record and can still usually get the repair done anyways.
Just ask for a case number to keep handy.
Also since there is AppleCare its always easy to just get into the Store to have them test it.
If no stores nearby Backup the Machine and have Apple Setup a Mail in Repair for you.
When you have the warranty still make sure you use it to the fullest.
Yes Genius bar appointment is perfect. Make sure to backup your Data.
You can book the Genius Bar with the AppleCare rep and get the issue documented and a case number all in one go. That way when you go to the Genius Bar they can review the notes the AppleCare person took.
Depending on the OS the hardware test can be done just by holding the D key during startup.
Thanks all for above replies. My MBP (early 2011) came w. the recovery discs. The Hardware Test is on disc 2 and I ran it....short version.....with no faults found. I've read that more thorough testing of graphics card is done on the long test, but I'm a bit pressed for time right now. This is no urgent problem EXCEPT for my immenent loss of Apple Care coverage. But, in view of that, I think I'm going to call Support in the morning and do what you guys recommend. From what I've also read, the store will have much more extensive diagnostic capabilities, and hopefully target-able to just the graphics card, since it's pretty time consuming to roll in all the other stuff (I've upgraded to 8GB of RAM) when one knows the problem isn't likely there. I have done the firmware upgrades that came out on this machine, so I could also use the online hardware test, but it sounds like that doesn't run any faster. Since I've only got 14 clean days of warranty coverage left, I think I'm going to go right to the pros for diagnosis on this one, minor though it is in terms of symptoms (so far anyway!). Thanks for the comments. I will post a f/u in due course re what I learn (I hate support discussion threads that just leave you hanging on how it actually came out!).
So I went to the Genius Bar with the history as outlined above. We had to watch my display for almost 10 minutes (while he checked various system stuff) before it would perform. But then it cut loose with a very convincing display of the faint, fuzzy groups of yellow lines moving slowly up the screen.
Tech pointed out that we were booted to an OS running on the store's server, NOT mine, so this ruled out software problems in one stroke. He said he'd never seen anything quite like it but felt it was EITHER: video "card" section of the main logic board (all on one in a MBP) OR a failing display. He said one or both would be replaced.
Two days later, picked up my MBP: problem solved! Tech said they connected my laptop to an external display (which I had not tried because I didn't have one available.....though maybe a tv could have subsituted, now that I think of it!) and NO PROBLEM driving the external lcd display. So they replaced my 15" lcd display and problem is gone. "Bill" was about $600, parts and labor, but Apple Care picked it up (with 6 days left to run on the coverage!).
So that's the follow-on for this problem, fyi.