Wall displays almost universally assume a mostly flat and static shape. We ask two questions: Would people choose a flat display for a given interaction scenario and, if not, what are the display shapes they actually prefer? We conducted a design study around these two questions. Our results show that participants designed different screen shapes that varied based upon peoples' distance from the display and the content shown. Shapes ranged primarily between flat, separated, concave, L-shape and convex displays. Based on our findings, we designed a dynamic display that changes to these and other configurations. Shape-shifting is controlled either by explicit interaction (where the display responds to hand gestures) or implicitly (where the display infers a shape based both on its content and the sensed positions of the people around it). Overall, we contribute: a study that motivates research on shape-shifting wall displays, and a shape-shifting display system that responds to explicit and implicit controls to match particular activities.