We shall discuss closed string solutions in the bulk of AdS space that are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincare patch.