We present deep optical images of the Large and Small Magellanic Clouds (LMC and SMC) using a low cost telephoto lens with a wide field of view to explore stellar substructure in the outskirts of the stellar disk of the LMC (< 10 degrees from the LMC center). These data have higher resolution than existing star count maps, and highlight the existence of stellar arcs and multiple spiral arms in the northern periphery, with no comparable counterparts in the south. We compare these data to detailed simulations of the LMC disk outskirts, following interactions with its low mass companion, the SMC. We consider interaction in isolation and with the inclusion of the Milky Way tidal field. The simulations are used to assess the origin of the northern structures, including also the low density stellar arc recently identified in the Dark Energy Survey data by Mackey et al. at similar to 15 degrees. We conclude that repeated close interactions with the SMC are primarily responsible for the asymmetric stellar structures seen in the periphery of the LMC. The orientation and density of these arcs can be used to constrain the LMC's interaction history with and impact parameter of the SMC. More generally, we find that such asymmetric structures should be ubiquitous about pairs of dwarfs and can persist for 1-2 Gyr even after the secondary merges entirely with the primary. As such, the lack of a companion around a Magellanic Irregular does not disprove the hypothesis that their asymmetric structures are driven by dwarf-dwarf interactions.