Currently, data visualization systems employ a variety of techniques and user interface components to facilitate interaction on mouse-based desktop and laptop computers. However, the same is not true for interaction on touch-based devices such as tablets and mobile phones. Data visualization has yet to become pervasive there and it is not clear what interactive operations should be provided and how they should be performed. In this paper, we discuss an approach to designing interactions for touch- based visualizations employing user-suggested gestures. This design space for touch gestures on data visualizations is especially rich, perhaps more so than many expect.