A method and apparatus for operating a multi-user interactive display system including a display having a touch-sensitive display surface. A position is detected of each contact site at which the display surface experiences external physical contact. Each contact site's position history is utilized to compute velocity data for the respective contact site. At least one of the following is utilized to identify occurrence of one or more user gestures from a predetermined set of user gestures: the position history, the velocity data. Each user gesture corresponds to at least one predetermined action for updating imagery presented by the display as a whole. Action is commenced corresponding to the identified gesture. Responsive to a user gesture terminating with a nonzero velocity across the display surface, action is corresponding to the gesture is continued so as to simulate inertia imparted by said gesture.