Split-flap displays are found, most commonly it would seem, on older-style alarm clocks. These displays rotate through a sequence of images (12 hours, for instance), showing items in order.
Time is one thing to display, but this largely-forgotten mechanism can be used for much more interesting purposes with modern electronics. Tom Lynch, who has been fascinated with this type of device since childhood, decided to build his own while studying at The University for the Creative Arts as an undergraduate. Building one turned out to be a lot of work: five years of learning mechanical design, manufacturing, and electronics.
Details of this journey are shown on the “unknown domain” website, or you can see a more succinct version here. This display, as shown in the video below, was used as part of an installation for the RIBA Regent Street Windows Project, where, according to their site, “unique and eye-catching displays demonstrate the innovation and creativity of architects while demonstrating the retailers’ commitment to quality design.”
If you think it would be cool to build your own, but aren’t ready to commit five years to the process, you could always modify one that’s already finished mechanically. Although a bit different, this “flip-dot” display might produce some inspiration.