We present the results from the analysis of a diffractive element with a quasi-periodic structure of phyllotaxis type. The output pattern obtained from such a diffractive element is characterized by an annular symmetry that can be used in different applications. We discuss the influence of the parameters defining the diffractive element geometry on the diffracted pattern, showing that the golden angle interval is optimal for an arrangement of circular elements. We also demonstrate that the properties of the diffraction pattern can be changed by using proper non-binary phase functions for the diffractive element to obtain a non-symmetrical pattern, to reduce the zero order or to increase the intensity in a specific diffraction order.