Not sure if this word is used as commonplace, but "sloshing" was introduced to me as a student. It's that time where you consciously put a problem into the back of your mind b/c you can't immediately, while at your minds forefront, conceive an answer.
Inevitably, a solution will come to you as you casually think about your problem while doing some other activity. Driving, mowing the grass, listening to music, etc.
So I ask, where do you do your best "sloshing"? (For me...it's while driving)
The morning shower. Don't know why but I can struggle with a problem all day and make no progress and solve it in two minutes in the shower.
Secondary would be in the dead of night. I'll just wake up with an answer that I've been chewing on. I keep a notepad nearby so I can write it down and go back to sleep - otherwise I just spend the rest of the night working the problem out in detail.
Many solutions occur to me in the time between first waking up and finally getting out of bed. Something about the quiet of morning after a night of sleep helps a lot.
I spend a lot of downtime playing tetris and listening to music on my laptop. I'll play some introspective music (usually jazz or classical) and let the bricks fall. I do a lot of my best thinking playing tetris, oddly enough.
On a more pedestrian level, I spend a good portion of my day walking around campus and the U district in Seattle between classes and work. This in conjunction with more music tends to lead to what you refer to as sloshing.
Generally the answers come to me as soon as I've gotten too far from the keyboard to attempt implementing them. Common examples are: two minutes after leaving work, five minutes after heading out to lunch.
Here's an (non-scientific) article on the subject...From the article:
"If you don't give the brain breaks, it will take them", he says, "in the form of loss of concentration, or what we call a mental breakdown."
I'm pretty sure some studies have been done about the importance of "sloshing" as you put it. I think my brain is taking one of those involuntary breaks as we speak...can't seem to find the links.
When I've walked away from the problem. Often when I've gone outside. So I always carry some 3x5 index cards and pen.
For those times that inspiration strikes in the shower, an inexpensive "diver's slate" (a rough plastic surface with a pencil attached by a rubber tube) works well for jotting down notes.
When going to sleep. It's bad, because by the time i figure it out, im way too tired to get back to the computer. So i always tell myself "ill try it in the morning". But when i wake up, i don't fully remember all of it and/or where i left off the night before.
On the toilet. Seriously. I can stare at a problem for an hour not knowing how to solve it and go for a quick bathroom break where the answer just pops into my mind.
My three most important productivity tools are long walks, hot showers and frequent naps. (The naps offset the marathon coding sessions where I'm so deep in codespace that I don't notice that the sun has risen and set.)
Playing video games and watching TV/movies tend to be my best "sloshing" situations. The video games tend to be a combination of real-time strategy(Age of Empires or Starcraft), action RPG(Diablo II or Guild Wars or Titan Quest), or Yahoo! Games(pool, Euchre, Literati, Bridge, or Reversi).