I play fingerstyle guitar (beginner-intermediate level, I don't really know any music theory), and often times I find that I'm browsing my email or something with one hand, and the other is free to play around with the strings. But obviously, I can't play chords with one hand. So do you guys know of any cool picking patterns or just in general things to do with the picking hand when the chord hand is busy doing something else?
If you're looking to practice right hand (or picking hand) patterns there is a work in the classical guitar repertoire,
La Tecnica Degli Arpeggi, Guglielmo Papararo.
It is comprised of just about every possible fingering pattern played on the open string. Of course if you tune your guitar to a open tuning you'll be fingering some chord other than an E minor 7 (add 4), or E min 11.