Reminds me of my cat, he has decided that the best place to sit is under our bed. Not just under the bed though, he tore a hole in the fabric under our boxsprings and crawls up in there. I’ve blocked up the hole so he can’t get in there and now he sits batting at the area and whining.
Little brat.
Every bed I’ve ever owned, and my mom’s bed back when I still lived at home, had the same thing happen. Hole in the fabric under the boxspring, and the cat goes up inside. This is pretty much the only reason the cats aren’t allowed into my bedroom. My boyfriend thinks I’m exaggerating the risk, but I swear, I’ve had a whole long progression of cats do the same thing to a whole progression of beds.
The corner in the wall doesn’t meet at 90 degrees? 
have you checked your cabinets lately?
call me crazy, but it sure looks to my eye that your overlords are looking UP. :eek:
It’s hard to tell from the photo, but where they are sitting, and where they are looking, they’d be seeing a reflection of the tortillas and other stuff that is sitting on top of the microwave (and that only vaguely–it’s really hard to see a reflection in those tiles without direct lighting). Yes, I did get up in there and put my head where theirs were and check. Edited to add: in the photo you are seeing the shadow of the cat’s head/ears on the tile, not the reflection. And no, they’re not staring at their shadows, because as I have said they do this all the time in the dark.
Scubaqueen: We use those cabinets daily. We’ve already checked (repeatedly) all of the cabinets for signs of mice or bugs or anything and found nothing. Most of the time they seem to be looking at the wall just to the left of the microwave. Sometimes they glance upward, sometimes they look back over their shoulder as if to say “what? what are you looking at?” but mostly it’s staring at the wall.
My dog does this sometimes. Either sitting and staring, or curled up with his face in a corner. He doesn’t do it with a particular spot, tho. I guess sometimes he just likes corners.
One of our cats likes to stare at the hallway wall, and sometimes runs back and forth along it. The entire length of the hallway is the dividing wall with the neighbouring apartment (long-style apartment, all the rooms to the right, in a row). Either she listens to the neighbours walking around (they might have pets too, I don’t know) or there are mice between the walls. We have had mice come into our pantry during the cold snaps last winter, but since we plugged up the hole, we haven’t had any signs. I do think it is likely, though, that a few mice are still roaming around back there. It is a really old building (90 years or so) and there must be a million entryways for them!
When the sun is hitting the kitchen wall just right, my cat will look up from his food bowl and become so fixated on his own ear shadows that I have to rattle the bowl to regain his attention. Then he does it again.
My wager is they can hear termites chewing in the wall. Get a stethoscope!
I had a cat do that once and had her kittens there. I left her alone for one day but then decided to remove her and the kittens to a better spot. I had to remove the entire fabric to get her and the babies out. It was a good thing I did as one of the babies had died 
Awww!