A long walk

Alice has lived forever in a universe with an infinite road that has a beginning and no end, and is marked every mile. Every day of her life, by an irresistable longing, she has followed these rules: If somehow she’s not on the road, she goes to mile zero on the road. If she is on the road, she walks a mile in the endless direction of the road. Besides the movement required by 1 and 2, she stays…