An algebraic starscape is a plot of algebraic numbers–complex numbers which arise as solutions to polynomial equations with rational coefficients. There are many mathematical or artistic choices one can make when creating an algebraic starscape, from choosing polynomials to sample from, to deciding how to color and size the algebraic integers you obtain. In this talk, we will explore some of these different perspectives, observing that the visual outputs can vary widely, and illustrating how one can use this viewpoint to extract new arithmetic results.