Dynamically Interactive Visualization (DIVI) is a novel approach for orchestrating interactions within and across static visualizations. DIVI deconstructs Scalable Vector Graphics charts at runtime to infer content and coordinate user input, decoupling interaction from specification logic. This decoupling allows interactions to extend and compose freely across different tools, chart types, and analysis goals. DIVI exploits positional relations of marks to detect chart components such as axes and legends, reconstruct scales and view encodings, and infer data fields. DIVI then enumerates candidate transformations across inferred data to perform linking between views. To support dynamic interaction without prior specification, we introduce a taxonomy that formalizes the space of standard interactions by chart element, interaction type, and input event. We demonstrate DIVI's usefulness for rapid data exploration and analysis through a usability study with 13 participants and a diverse gallery of dynamically interactive visualizations, including single chart, multi-view, and cross-tool configurations.