Have A Toddler?

Just wondering here: when walking along with my one yr old on my hip, she will watch my free arm swing, and pretty soon her outside arm is swinging along in imitation of mine. Then she will look up at me and grin in the most companionable sort of way. As far as I can remember none of my bigger kids did this, though BOTH of my Ethiopian daughters do/did it– and it is so darned cute. It just got me wondering if other people have noticed this with their little ones. So how about it? Does your baby do this??