During development, plant aerial organs are produced along the stems following stereotyped patterns. This so-called phyllotaxis is initiated at the shoot meristem, which contains the stem cell niche: organs are produced iteratively and their precise position is thought to depend on dynamic interactions with preexisting organs. These interactions would notably result from inhibitory fields generated by the polar transport of the plant hormone auxin. To investigate whether other factors than auxin regulate phyllotaxis, we studied the potential role of cytokinin signaling. We developed a new pipeline of methods based on statistics to analyze phyllotactic patterns. This approach allowed us to identify phyllotactic perturbations in mutants of the AHP6 (ARABIDOPSIS HISTIDINE PHOSPHOTRANSFER protein 6), an inhibitor of cytokinin signaling that suggested perturbations in the plastochron, the time between two organ initiations. This was further confirmed using confocal live-imaging. We demonstrated that AHP6 controls the regularity of the plastochron, and our results suggest that the defective phyllotaxis in ahp6 is caused by concomitant initiations of two or three organs in the meristem. Interestingly, AHP6 is expressed in organs and the protein can move beyond these domains, generating cytokinin signaling inhibitory fields. To explore further the putative role of these secondary fields, we generated a mathematical model of phyllotaxis. This suggested that plastochron instabilities could be caused by noise affecting the threshold at which meristematic cells are recruited into organs. Inhibitory fields generated by AHP6 could filter out the effect of noise by modifying the kinetics of early organ emergence. Consistently, the properties of AHP6 fields fit the model predictions and our experimental data show that AHP6 and cytokinin modulate auxin signaling during organ emergence. We thus propose a model in which auxin transport and signaling robustly control organ positioning but generates plastochron instablities in noisy backgrounds. In this scenario cytokinin inhibitory fields would stabilize the rhythmicity of organ initiation, ensuring a robust coupling of space and time during pattern formation.