Disclaimer: I do not and never will own Doctor Who. I only own this story and am making no profit from it.
This is just funny randomness and is not to be taken seriously.
Sleeping Is Cool
Travelling in the Time Vortex meant that the Doctor wasn't held by such limitations as 'daytime' and 'night-time'. After all, why finish something the next 'day' and rest in between, when you can fix it late at 'night' and then drink some coffee and run on caffeine until your friends get up? Caffeine, sugar and adrenaline, that was all he needed to keep himself bouncing. He was the Lord of Time, and time was not the boss of him.
Besides, he was working on a really important project that couldn't be set aside for something as dull as sleeping. The Doctor was building a device that predicted the future. It was all very complicated, measuring oscillations in the causal nexus and all that, but basically it was like a lie detector except that it told your future. It was really like that, of course. It didn't tell the future so much as narrow down a multitude of possible outcomes until you had only one, and even then it might not be the one that happened to you. But it would happen to you in some version of reality.
As for why he was building this device; well, did he need a reason? The Ponds were asleep, the Doctor was bored, and things just sort of…occurred. Sixteen hours later, the triumphant extra-terrestrial bounded into the kitchen. "Morning, Ponds!" he cried cheerfully. Amy gave him a death glare that would send a Silurian running, and turned back to her coffee. Rory was a little bit mellower. "Good morning Doctor. Did you sleep alright?" he asked. "Pft. Who needs sleep? I've been revolutionising" he informed them.
Amy and Rory finally noticed the device that the Doctor was cradling in his arms. "What's that?" asked Amy, perking up a little. "I built it last night. You strap this around your wrist, see, and the machine does a lot of wibbley wobbley stuff and hey presto, tells your future! I call it the 'really interesting very extraordinary reality sensing…device" he explained proudly. "So basically…you're a time travelling alien, who's built a machine that tells the future, and you've named it after River by using a load of adjectives instead of proper technical terms".
"….shut up. So, who wants to try it out?" the Doctor asked, smiling at them like an eager five year old. "Sure" said Amy, holding out her wrist. The machine whirred and beeped, then spat out a strip of paper. The Doctor tore it off and read the following alive. "You will spend the next few hours with six feet. Well, that will be interesting I'm sure". Amy scoffed. "Whatever. I bet it just came up with something random. The really very un-extraordinary random sentences device" she retorted.
The Doctor looked scandalised. "Don't diss the RIVERD- which I did not name after River, and if I did it was entirely subconscious! Also, your acronym is rubbish" he argued back. Rory ate some toast. "This is the second time you've made some bizarre device in two days. I'm starting to think you're just avoiding going to bed" Amy said sarcastically. The fact that the Doctor hated sleeping was the TARDIS's worst kept secret. "You can think that if you like, Amelia" he replied patronisingly. Rory ate some more toast.
That day, RIVERD's prophecy actually did come true. The Doctor somehow managed to mistake the co-ordinates for Aphelion with those for a six legged race at a county fair. Apparently the chance to compete in the silliest race ever devised was something the Doctor had always longed for, surprise surprise. He was so smug at his machine being correct that Amy purposely tripped them up a foot away from the finishing line. Then she proceeded to snog Rory in a way that had parents covering their children's eyes, and the Doctor flailing like a landed fish in his attempts to extricate himself from the tangle of limbs.
Thirty six hours later, Amy insisted on having a beauty nap. Rory suggested that he go and keep her company, but really he just didn't want to be alone with the Doctor. That was just…too awkward. Sometimes the Doctor pitied humans, with their need for so much sleep. He, on the other hand, could stay awake for – he yawned. But it didn't mean he was tired, far from it. He felt perfectly fine, apart from his blurring vision and; were his fingers trembling? No, it was just his imagination.
The TARDIS made an odd noise that vaguely sounded like a snore. The Doctor looked up at the Time Rotor and said "Don't tell me, you want me to go to bed". She beeped as a 'yes'. "No fear. I'm not even tired" said the Doctor, stubbornly. He reached behind him for his sonic screwdriver, but it wasn't there. Looking around, the Doctor spotted it rolling away down the steps and gave chase. The screwdriver stayed just out of his reach the entire time, rolling through the corridors as if it was being dragged on an invisible string.
"Not…funny…now give it back" he panted fifteen minutes later. The lights flickered as a 'no'. Up ahead, the sonic rolled through an open door and into a darkened room. The Doctor groaned, and walked up to the threshold. He was just about to step inside when the floor tilted violently, throwing him through the doorway. He fell down like a stone, yelling his head off, and landed on something springy. So springy, in fact, that he bounced three times.
The lights came on, and the Doctor found himself lying in a hammock, made of vines, in a rainforest. His trusty sonic screwdriver was wedged between two branches. One scan of his surroundings told the Doctor he wasn't in a real rainforest, thank goodness. He hadn't forgotten the time the TARDIS had moved the dimensional transmitter to the door of his shower. He doubted that the six thousand people come to listen to Beethoven in the Royal Opera House had forgotten that incident either.
It would be easy to climb back out of the room; at least, if his foot wasn't caught in the vines. No matter how hard the Doctor tugged at them, they wouldn't break loose. In fact, they seemed to get tighter. "So is this how it's gonna be? You're gonna just keep me here until I fall asleep" he asked the TARDIS, and she hummed smugly. The Doctor groaned in defeat and lay back in the makeshift hammock. He supposed he brought this on himself, with all his complaints about sleeping being boring. He couldn't very well call this boring.
A few weeks later, the Doctor found himself once again at the end of his sleeping tether. He went through all the motions; insisted he wasn't tired, ran around all night (although sometimes it was more of a stagger) and so on. Eventually he gave up and went in search of the rainforest bedroom. It appeared to have vanished entirely. "Oh come on. What was the point in creating a room like that if you never let me use it?" the Doctor demanded. He'd looked into all the rooms in this corridor five times now.
"I'm tired" he moaned petulantly, leaning against the door to the kitchen. It rumbled under his shoulder, and swapped in the blink of an eye with a door of darker shade. The Doctor pushed the door open, and found himself face to face with a lionfish of all things. Well, a holographic one at least. The rainforest had become a coral reef. "I get it. Sleeping on a seabed, ha, ha. Very funny, old girl" he said sarcastically.
The next morning, the Doctor was rather subdued when he came into the kitchen. "Morning, Doc" said Amy. "Doc's a dwarf. I'm the Doc-tor" he replied. "Okay, Doc-tor. What have you been doing all night then?" she asked. The Doctor said something she never thought she'd hear him say. "I've been asleep, Amelia. Sleeping is cool".
A/N: The 'dimensional transmitter' is a bit of head-canon that says that the doors are actually like teleporters, sending you from the inner dimension to the outer dimension. Or something like that.