The plant root cap, surrounding the very tip of the growing root, perceives and transmits environmental signals to the inner root tissues. In Arabidopsis thaliana, auxin released by the root cap contributes to the regular spacing of lateral organs along the primary root axis. Here, we show that the periodicity of lateral organ induction is driven by recurrent programmed cell death at the most distal edge of the root cap. We suggest that synchronous bursts of cell death in lateral root cap cells release pulses of auxin to surrounding root tissues, establishing the pattern for lateral root formation. The dynamics of root cap turnover may therefore coordinate primary root growth with root branching in order to optimize the uptake of water and nutrients from the soil.