Maybe you should take George out to a bar once in a while.
I love you Internet!
The second link of Googling how to tell the difference between a cat and a meatloaf brought up the illustrationI was thinking of.
The artist is B. Kliban. Apparently, he was well-known. I like the (uncited) trivia bit: “According to Art Spiegelman, Kliban invented the form of cartoon, popularized by Gary Larson and others, of a single panel with a third-person caption describing the action.”
Mine catloafs all the time in cool weather, and in fact one of his favorite ways to sleep is to just drop his chin down and doze off with his legs and tail still tucked in. I call that one the “cat wedge” because with his pointed nose expanding to big fuzzy butt he reminds me of a big cheese wedge.
I agree it’s probably to conserve heat, because in warm weather he usually sprawls out on his side to rest or sleep.
One of my family cats used to do this when she was sulking, we called it the stuffed turkey (not chicken, she was too plump to be a chicken).
I’ve never heard this position compared to a loaf, but from now on that’s what it is.
The reason, naturally, is that cats are born loafers.
I think it’s for heat too, to keep their legs and tail warm. When it’s hot outside they seem to choose the ‘dead bug’ position over the catloaf.
You’re welcome! 
Lion Couchant? But to answer the OP, who knows. Cats just do it.
I’ve not seen a cat do it in person, but apparently it’s not uncommon. See here, for example. It’s basically a fighting posture: he appears larger by turning side-on to you, wants to keep facing you, but still wants to be able to move around. Either you genuinely startled him and it’s a defensive mechanism or (more likely) he’s being playful; in either event, I would assume that whether he does it depends on his state of mind when you walk into the room.
One of our cats constantly loafifies, to the point that I’ve seen her lie down by going from a full standing posture to kneeling on her front legs, already tucking them in before the back half has even touched the floor. (Picture a camel kneeling down.)
I think the sideways dance is an invitation to play. Is your cat young, OP? Young cats get all cracked out sometimes, and tear-ass around for no apparent reason. They’re just being playful and energetic. 
I love catloafs. We’ve two, and they catloaf often. Most of the cats I’ve had do it. No idea why, but I love how they tuck their front paws in like that.
it also protects thier underbelly, and allows for a quick jump and run response.
Some non-feline animals also do that, for instance, sheep:
http://www.gilmertonfarm.com/images/onesheep.jpg
ETA:
and cows, although their legs are generally still visible underneath them.
Well, as long as they’re kneading their paws…
My kitteh tends to do this when he’s demanded to go out on the porch, but it’s really just a bit too chilly for him. I think it keeps his paws and tail warm. When he lays on the heater vents, he sprawls out belly up, with no regard whatsoever to the toothy pitbull who likes to nip at paws, tails, and whatever else she can get her teefs on.
Of the various feline creatures we have owned or fostered over the years, some have been near-constant loafers–even in warm weather–and others have never gone into loaf shape.
I think there’s a bit of protectiveness to the position more than of mere conservation of heat. Our second-youngest adopted cat likes to fill up one of the levels of the scratching post or find an obliging human to curl up next to. And the kitten we kept from the foster mom’s litter just doesn’t stay still long enough to go into loaf…when she falls asleep, it’s either in a tight ball or all stretched out (“pork tenderloin shape” as I’ve called it). Both cats grew up around humans–the kitten from literally Minute One of her life–and I suppose don’t feel the need to defend themselves.
Yes! LOL! That’s exactly what George does (though he is much bigger than the cat in that video and so it is ever the more intimidating.) Tail puffed up, double-sideways hop.
?!!?
I always thought that was a moment (or more) of Zen for a cat. Just the state of BEING. Or what TS Eliot called the contemplation of his name.
Llama’s too. Lady Chance and I refer to it as ‘the llama has retracted his legs’.
http://comegetyousome.com/photo/15353/llama-sitting.html
This place calls in Llamapillar.
Lynn, your explanation is the best so far.