I sometimes feel as though I do my best thinking while aimlessly wandering around... or when I'm waiting for trams. For this reason, I end up with lots of scrawlings on receipts or tram tickets. They're ideas that I simply cannot afford to forget, so they have to be written down!
It's not as though I'm necessarily relaxing in these situations, but I do feel like the different surroundings (and maybe the lack of other distractions) help me to contextualise and realise the intangible thoughts that have been floating around in my head (often for a number of days). I guess it is a bit like the sudden bolts of inspiration that can hit while in the bath or shower... that I had to relax in order to clarify an idea or sort out a problem.
(As a side note, I used to do maths problems in my sleep when I was at school. Going to bed after attempting to solve a difficult problem - my head still full and buzzing - was often the best way to get an answer. It was rare that I'd wake up with the exact answer in my head, but I'd always know what I'd done wrong the night before, and what I needed to do to solve it properly. To this day, I don't know if this was a healthy thing or not, but it did work. I just wish it worked with my designing!)
Speaking of side notes, this is another aspect of thought that really intrigues me... that we create branches of ideas in our heads, like vine tendrils... delicate webs of neurons...
...and that sometimes the very act of writing our thoughts down interrupts this incredible branching process and we lose some of what we'd thought in those moments. Even now, having written this, there's a niggling feeling of a lost, floating thought. How ephemeral our cognitive processes can be!