All visualization tools that display data as it is manipulated by a parallel, MIMD computation must contend with the effects of asynchronous execution. In some cases, this is done with the explicit simulation of a global clock but that is not always feasible. Here we propose a less restrictive mechanism in which logical time is manipulated in order to produce coherent animations of parallel program behavior. Our techniques ``interpret'' program behavior in light of user-defined abstractions and generate animations based on a logical rather than a physical view of time. In this paper, we have demonstrated the application of these techniques more generally to a variety of types of data visualizations.