Compare the representation (or self-representation) of at least two (2) Ptolemaic queens from Arsinoe II to Cleopatra VII. How are they represented, or how do they represent themselves? Does their iconography change over time (i.e., crowns, dress, attributes, poses, etc.)? Can you link elements of or changes in their representations in inscriiptions and documents to elements of or changes in their iconography? Are they associated (or do they associate themselves) with particular places or temples or gods or goddesses? Can you connect changes in their representation to the prevailing politics or the way in which ruler cult worked? Can you detect differences in messaging to differences in audience or meaning encoded in context or style?
You do not need to restrict yourself to plastic images, but you may also use inscriiptions, poems (e.g., Idyll 15 by Theocritus or the “Lock of Berenike” in Book 4 of the Aitia by Callimachus, known largely through Catulus’s translation, poem 66), or even (in the case of Cleopatra VII) representations by others after the fact, like Plutarch’s Life of Antony (but you must find a way to read such literary sources as communicating something about the queen’s (self-)representation, even if through a distorting lens).