Graph rewriting systems (GRSs) operate on graphs by substituting local patterns according to a set of rewriting rules. The apparent simplicity of GRSs hides an incredible complexity and turns the study of these systems into an involved task requiring high-level expertise. We designed PORGY, an interactive visual environment to fully support GRSs related tasks, exploiting a long historical tradition of GRSs with node-link representations of graphs. PORGY enables rule-based modeling and simulation steering through graphical representations and direct manipulation of all GRSs components. This paper contributes a design study and task taxonomy relevant to the interactive visualization of GRSs.