Thanks to MK for the prompt.
The slow death of purposeless walking, by Finlo Rohrer (BBC News Magazine)
... "There is something about the pace of walking and the pace of thinking that goes together. Walking requires a certain amount of attention but it leaves great parts of the time open to thinking. I do believe once you get the blood flowing through the brain it does start working more creatively," says Geoff Nicholson, author of The Lost Art of Walking.
"Your senses are sharpened. As a writer, I also use it as a form of problem solving. I'm far more likely to find a solution by going for a walk than sitting at my desk and 'thinking'."