A magma is an algebraic structure consisting of an underlying set and a single binary operation on that set. Much is known about specific families of magmas (semigroups, monoids, groups, semilattices, quasigroups, etc.) as well as magmas in general as treated in universal algebra. We seek to relate the study of magmas to the study of corresponding geometric objects. In order to do this we first analyze unary operations by way of their graphs. We show how function composition can be encoded by matrix multiplication, then generalize this to binary function composition. We characterize the spectra of the graphs of unary operations, show that all such graphs are planar, and present some initial results on the corresponding constructions for magmas.