  Dynamical transitions of the Acetabularia whorl formation caused by outside
calcium concentration is carefully analyzed using a chemical reaction diffusion
model on a thin annulus. Restricting ourselves with Turing instabilities, we
found all three types of transition, continuous, catastrophic and random can
occur under different parameter regimes. Detailed linear analysis and numerical
investigations are also provided. The main tool used in the transition analysis
is Ma \& Wang's dynamical transition theory including the center manifold
reduction.
