Thomas,
Thanks for so much your response.
The mask screen appeared twice when I went out of the room for a while leaving the computer on. These were several sinister looking primitive masks, some purple and green that looked like chalk drawings. I can't find anything like them in search images.
Each time the masks appeared, I cleared out the cookies, files in Safari and reset Safari, then shut down the computer, restarting it holding down the shift key.
On the possibility that the computer gets invaded when it sleeps, I stopped the sleep function.
The masks haven't returned in a couple of days - so I can't capture them for you.
Although the scary masks haven't reappeared, I have had some screen saver images of brightly colored discs appear that I did not select - and can't find in the apple files, instead of the beach photos I use as a screen saver.
This doesn't seem to be adware, because I ran AdMedic after the Apple tech support recommended it and it said my computer didn't have adware.
Thanks again!