A classical ferrofluid undergoes a Rosensweig - or normal field - instability resulting from a competition between gravity and surface tension, and magnetic interactions. As a result, above a critical magnetization, the ferrofluid forms ordered structures. We will present the experimental observation of the equivalent of this instability with a “quantum ferrofluid”: a dipolar BEC of dysprosium atoms. The instability arises here from a competition between the short-range isotropic repulsion characterized by the scattering length a and the dipole-dipole interaction, with a dipole moment of 10 µB for Dy. We drive this instability on a fully magnetized BEC by varying the scattering length on a Feshbach resonance. As a result of this instability, we observe the formation of ordered droplets ensembles. These structures show surprisingly long lifetimes of hundreds of ms.