My exercise research suggests our brains work better when we walk. Here’s one way to combine walking and writing:
While working on a paper, which was most of the time, [Niels] Bohr would select an assistant from among the young physicists in Copenhagen. The assistant, affectionately dubbed the victim, was supposed to sit in place while Bohr paced around the room, constantly puffing away at his pip, working and reworking his ideas, talking aloud as the idea took shape, trying and retrying to dictate his sentences to the victim.
From Faust in Copenhagen: A Struggle for the Soul of Physics by Gino Segre.
The modern version may be use of word recognition software with the computer screen on a wall or large TV. You walk back and forth in front of it. I have spent a lot of time writing while walking on a treadmill but it was noisy and tiring. Moreover, it was hard to start and stop and it was monotonous.