A long-running study involving 299 older adults (average age 78) has found that those who walked at least 72 blocks during a week of recorded activity (around six to nine miles) had greater gray matter volume nine years later. Gray matter does shrink as we get older, so this is not about growth so much as counteracting decline. Walking more than 72 blocks didn’t appear to confer any additional benefit (in terms of gray matter volume). Moreover, when assessed four years after that, those who had shown this increased brain size were only half as likely to have developed dementia (40% of the participants had developed dementia by this point).
(2010). Physical activity predicts gray matter volume in late adulthood.
Neurology. 75(16), 1415 - 1422.