iMac in Continuous Shutdown/Restart Loop

2011 iMac 27". While Mail and Safari open, reading a webpage, the screen suddenly went to a black and white vertically striped display. I waited a few moments to see if anything would happen, then the machine seemed to shutdown. But then it appeared to go into restart on its own. It doesn't fully restart though -- a screen appears with the dark gray apple and progress bar. It runs on this screen for a minute or two, then goes into shutdown and restart modes again.

Nothing new or different has been done to this computer in recent weeks.

Any ideas much appreciated.