Modular, repetitive structures are a key component of complex multicellular body plans across the tree of life. Typically, these structures are prepatterned by temporal oscillations in gene expression or signaling. Although a clock-and-wavefront mechanism was identified and plant leaf phyllotaxis arises from a Turing-type patterning for vertebrate somitogenesis and arthropod segmentation, the mechanism underlying lateral root patterning has remained elusive. To resolve this enigma, we combined computational modeling with in planta experiments. Intriguingly, auxin oscillations automatically emerge in our model from the interplay between a reflux-loop-generated auxin loading zone and stem-cell-driven growth dynamics generating periodic cell-size variations. In contrast to the clock-and-wavefront mechanism and Turing patterning, the uncovered mechanism predicts both frequency and spacing of lateral-root-forming sites to positively correlate with root meristem growth. We validate this prediction experimentally. Combined, our model and experimental results support that a reflux-and-growth patterning mechanism underlies lateral root priming.