  Generative AI for the creation of images is becoming a staple in the toolkit
of digital artists and visual designers. The interaction with these systems is
mediated by \emph{prompting}, a process in which users write a short text to
describe the desired image's content and style. The study of prompts offers an
unprecedented opportunity to gain insight into the process of human creativity.
Yet, our understanding of how people use them remains limited. We analyze more
than 145,000 prompts from the logs of two Generative AI platforms (Stable
Diffusion and Pick-a-Pic) to shed light on how people \emph{explore} new
concepts over time, and how their exploration might be influenced by different
design choices in human-computer interfaces to Generative AI. We find that
users exhibit a tendency towards exploration of new topics over exploitation of
concepts visited previously. However, a comparative analysis of the two
platforms, which differ both in scope and functionalities, reveals some stark
differences. Features diverting user focus from prompting and providing instead
shortcuts for quickly generating image variants are associated with a
considerable reduction in both exploration of novel concepts and detail in the
submitted prompts. These results carry direct implications for the design of
human interfaces to Generative AI and raise new questions regarding how the
process of prompting should be aided in ways that best support creativity.
