In a method and a magnetic resonance (MR) system to generate MR images based on an MR measurement of the magnetic resonance system, MR data are acquired in three-dimensional k-space along straight lines proceeding in parallel. Each of these lines is defined by a point in a plane which intersects each line and that is situated orthogonal to each line. The points in the plane are arranged such that a distribution of the points obeys spiral phyllotaxis.