Analytic provenance can be visually encoded to help users track their ongoing analysis trajectories, recall past interactions, and inform new analytic directions. Despite its significance, provenance is often hardwired into analytics systems, affording limited user control and opportunities for self-reflection. We thus propose modeling provenance as an attribute that is available to users during analysis. We demonstrate this concept by modeling two provenance attributes that track the recency and frequency of user interactions with data. We integrate these attributes into a visual data analysis system prototype, ProvenanceLens, wherein users can visualize their interaction recency and frequency by mapping them to encoding channels (e.g., color, size) or applying data transformations (e.g., filter, sort). Using ProvenanceLens as a design probe, we conduct an exploratory study with sixteen users to investigate how these provenance-tracking affordances are utilized for both decision-making and self-reflection. We find that users can accurately and confidently answer questions about their analysis, and we show that mismatches between the user's mental model and the provenance encodings can be surprising, thereby prompting useful self-reflection. We also report on the user strategies surrounding these affordances, and reflect on their intuitiveness and effectiveness in representing provenance.