Persistence of Memory

Connect the two black dots by a path which travels horizontally and vertically between cell centres. The path may not touch itself, even at a point, considered as a path of full cells. (The path is “snake-like”.) 

The grid contains some shaded areas, each of which must be visited by the path. Whenever two areas are the same up to translation (but not rotation), the path must be exactly the same within both copies.