I remember years ago reading an interview with Joe Satriani who said he used to just sit and noodle, and end up coming up with what he called Satch Boogies. It's where the song of the same name came from, I think.
I was sitting with the acoustic bass yesterday, which I've enjoyed a lot more since I strung it with electric strings (elite blue labels, very light) than the phosphor bronzes I had on there - the bronze strings always felt sticky, uncomfortable and I didn't like the smell (which I'm guessing is copper). I fiddled around with some shapes as usual, climbing around, but ended up doing some kind of open E boogie thing with high neck register figures in between, which turned out to be loads of fun on a sunny day.
Anyone else do this when they're not trying to overtly write or learn something? Those moments when you're just indulging in the pure playfulness of music? I need to make more time for those moments.