This paper presents a framework to better understand and analyse interaction and interactivity within the practices that fall under the broad descriptor of digital art. It is a context in which the main theoretical concepts of human-computer interaction do not necessarily apply, since it often aims at creating interactions that are not intended for the user to control a system, but to establish a sort of dialogue between both. We present a framework with three levels of conceptualization: participants, elements and attributes. The first refers to the audience, the artwork itself and the artist, here at the role of the interaction designer. A series of elements, understood as the key aspect regarding the design of interaction, is assigned to each of these participants. Finally, the attributes further refine the detail of the analysis. The framework has been applied and validated through a group of experts that have implemented it by analysing a series of interactive digital art projects. The results show that the proposed framework is useful for understanding and intersecting interaction design with digital (interactive) art. We can, therefore, conclude that the proposed framework enables the analysis of various key attributes related to the audience, the artwork, and the artist in interactive art, in order to evaluate the clarity and ease of use of the proposed interactivity.