Self-similarity and scaling in two models of phyllotaxis and the selection of asymptotic divergence angles

► Scaling and self-similarity found in the divergence spectrum of two models of phyllotaxis. ► Limit of high organ density behaves like critical point in second order phase transitions. ► Universality of quantitative properties of phyllotaxis is related to critical behaviour. ► Mechanism identified that explains preferential selection of divergence angles observed in plants.