The self-assembly morphologies of various complex architectured miktoarm star copolymers consisting of more than two components has been investigated using dissipative particle dynamics simulations. The star topology of such molecules allow a wealth of new structures to be controllably realized as a function of composition, interaction parameters and molecular architecture. Here a number of highlights are presented showing many novel kaleidoscopic morphologies, including 2D tiling patters and 3D networks many of which show hierarchical features, i.e. ordering on multiple length scales. Several examples are extensions of the well-known bicontinuous structures P, D and G found in many natural and synthetic two-component systems.