Phyllotactic structures in radially growing spatial symmetry breaking systems

Phyllotactic patterns, i.e. regular arrangements of leaves or seeds around a plant stem, are fascinating examples of complex structures encountered in Nature. In botany, their symmetries develop when a new primordium periodically grows in the largest gap left between the previous primordium and the apex. Experiments using ferrofluid droplets have also shown that phyllotactic patterns can spontaneously form when identical elements repulsing each other are periodically released at a given distance from an injection center and are advected radially at a constant speed. A central issue in phyllotaxis is to understand whether other self-organized mechanisms can generate such patterns. Here, we show that phyllotactic structures also develop in the large class of spatial symmetry-breaking systems giving spotted patterns with an intrinsic wavelength, in the case of radial growth. We evidence this experimentally on chemical precipitation patterns, and numerically on two different models describing reaction-driven phase transitions and spatial Turing patterns, respectively. A generalized method for the construction of this new family of phyllotactic structures is presented, which paves the way to discover them in large classes of systems ranging from spinodal decomposition, chemical, biological or optical Turing structures, and Liesegang patterns, to name a few.