Abstract Rhythmic patterning is central to the development of eukaryotes, particularly in plant shoot post-embryonic development. The plant hormone auxin drives rhythmic patterning at the shoot apical meristem, but the spatio-temporal dynamics of the auxin gradients is unknown. We used quantitative imaging to demonstrate that auxin provides high-definition graded information not only in space but also in time. We provide evidence that developing organs are auxin-emitting centers that could self-organize spatio-temporal auxin gradients through a transport network converging on the meristem center. We further show that a memory of the exposition of cells to auxin allows to differentiate temporally sites of organ initiation, providing a remarkable example of how the dynamic redistribution of a morphogenetic regulator can be used to create rhythmicity.