In vascular plants, the arrangement of organs around stems generates geometric patterns called phyllotaxis. To achieve such regular patterns, the formation of organs in shoot apical meristems must be tightly coordinated in space and time. In the model plant Arabidopsis thaliana as in the majority of species, single organs are initiated successively at a divergence angle from the previous organ close to the canonical angle of 137.5°, producing a Fibonacci spiral. To understand the genetic control of this process, we identified a mutant impaired in cytokinin signaling, with obvious defects in phyllotaxis. We measured divergence angles between organs along the stems of wild-type and mutant plants. Surprisingly, sequences of measured divergence angles exhibit segments of non-canonical angles in both genotypes, albeit in lesser extent for wild-type. We thus designed a pipeline of methods for analyzing such perturbations and applied it to both wild-type and mutant plants. The models used in this pipeline combine a sub-model representing perturbations patterns (either a variable-order Markov chain or a combinatorial model) with von Mises distributions representing measurement uncertainty. Our analyses show that the segments of non-canonical angles in both wild-type and mutant plants can be explained by permutations involving 2 or 3 consecutive organs. Divergence angle sequences take the form of a concatenation of baseline and permuted segments where a permuted segment corresponds to the chaining of 2- or 3-permutations. The length of baseline segments between two permuted segments is highly structured and reveals unexpected patterns which depend on the nature of the permutation (2- or 3-permutation) that delimits the baseline segment. We also report significant individual deviations of the level of baseline segments with reference to 137.5°, demonstrating that each plant generates a stable divergence angle which is not necessarily the canonical angle. Further biological ex