Phyllotaxis as a Dynamical Self Organizing Process Part III: The Simulation of the Transient Regimes of Ontogeny

In two previous articles [Douady & Couder (1996a,b)] two iterative systems were defined, based respectively on hypotheses developed by Hofmeister (1868) and Snow & Snow (1952). It was shown that in the latter model all the variety of the spiral, whorled and multijugate patterns observed on botany could be obtained as steady regimes of the iteration. In this third article, several of the characteristics transient evolutions observed during the ontogeny are revisited. In the framework of the iterative system of Snow & Snow these evolutions can be reproduced, provided realistic initial conditions and time variations of the parameters are imposed.