I never thought about it being a "zen" thing but I've done this sort of doodling since I was in middle school and come to think of it, I'd do it when I was nervous, upset, or overwhelmed. ( I usually 'doodle' when I'm bored)
Pinner said: "An idea has formed! Make a journal designated specifically for doodles based on a quote. Just write an interesting, important, nonsensical, etc. quote that fits your current mood, then doodle around it!