In multi-component lipid mixtures, macro-domains can be directly observed with light microscopy, but nano-domains cannot. Monte-Carlo simulations of liquid-disordered + liquid-ordered phase separation, using a competing-interactions model, can simulate various types of phase morphologies including nano-domains. These simulations capture a more realistic picture of nano-domains as irregular clusters rather than smooth, round disks. On a curved vesicle, when line tension and the competing interaction of bending energy are of similar magnitude, modulated phase patterns occur Current work focuses on studying the various morphologies when competing interactions of line tension, bending energy, and dipole-dipole repulsion form nano-domains.