In this work, we propose a new set of generic curves described as nth order rose curves as candidates for metamaterial's inclusions. The proposed contour and the method to characterize them can be considered as a generic topology and design procedure to realize artificial magnetic material meeting specific constraints without extensive and full-wave simulations. Numerical examples has been provided to demonstrate the effectiveness and design efficiency when the nth order Rose curves are used to design AMM. The new curves, not only provide significant design flexibility, but also provide features that are not present in traditional topologies, most pronouncedly, a wider band over which the negative permeability is achieved with minimized dispersion.