I wanted to display the photo for a user profile - there a URL for that!
Short and sweet today, add this to your site address and you will get the users picture:
/_layouts/15/userphoto.aspx?size=L&accountname=name@email.com
Or through Delve:
/_vti_bin/DelveApi.ashx/people/profileimage?userId=name@email.com&size=M
Where the size parameter is in T-shirt sizes; S, M or L.