  Phyllotactic states are regular lattice-like structures on cylinders and are
a botanical classification scheme. In this communication, we report a sequence
of transitions between phyllotactic states for particles with a repulsive
particle-particle interaction on a cylindrical geometry at zero temperature. We
can infer the transition points as a function of density via Monte Carlo
simulations, as well as the mathematical descriptions of the ground states. The
lattices we generate are described as phyllotactic states that fit onto the
cylindrical surface as a set of helical chains. Our analysis shows how all
state energies lie on the same parabola which we exploit to find the
transitions.
