Visualization is an effective tool for understanding the execution of complex programs. Over the course of a visualization session a user may employ a wide range of graphical representations. Adaptable visualization displays are needed to meet these diverse interests and applications. This paper presents an approach that supports interactive creation and refinement of visualizations via on-screen manipulation of existing visual representations of the program. By acting upon visualizations on the screen, users control what aspects of the computation and what properties are displayed. An action modifies the visualization in a given program state, but users need to have a means of defining how the visualization reacts to changes in the program state. We present a manner of specifying the effect of actions on a visualization for future program states. To achieve their effect and update the program representation, actions are automatically re-applied, in the order they were performed, for each state of the computation. The interpretation of user action is based on a model for reasoning about visualizations that focuses on what information is visually communicated and is independent of the exact choice of graphical elements. We define a set of operations on the model that allow users to take advantage on the information on the screen and explore related parts of the computation.