Interactive visualization has become a powerful insight-revealing medium. However, the close dependency of interactive visualization on its data inhibits its shareability. Users have to choose between the two extremes of (i) sharing non-interactive dataless formats such as images and videos, or (ii) giving access to their data and software to others with no control over how the data will be used. In this work, we fill the gap between the two extremes and present a new system, called Loom. Loom captures interactive visualizations as standalone dataless objects. Users can interact with Loom objects as if they still have the original software and data that created those visualizations. Yet, Loom objects are completely independent and can therefore be shared online without requiring the data or the visualization software. Loom objects are efficient to store and use, and provide privacy preserving mechanisms. We demonstrate Loom's efficacy with examples of scientific visualization using Paraview, information visualization using Tableau, and journalistic visualization from New York Times.