PHYLLOTAXIS AS A DYNAMICAL SELF-ORGANIZING PROCESS .2. THE SPONTANEOUS FORMATION OF A PERIODICITY AND THE COEXISTENCE OF SPIRAL AND WHORLEDPATTERNS

The conditions for the appearance of a new primordium put forward by S now & Snow (1952) are shown to form the rules of a dynamical iterative system more general than that based on Hofmeister's hypotheses (1868) . This system is simple, generic and compatible with several of the id eas about the possible nature of the interaction between primordia. By numerical simulation, it is demonstrated that this system is sufficie nt to spontaneously generate time periodic regimes in which the succes sive elements are organized either in Fibonacci spiral or in whorled m odes of growth. We show that the dynamical system generally selects th e pattern with the densest packing. The effect of the geometrical shap e of the apex and of the primorida on the stability of the opposite de cussate phyllotaxy is pointed out. (C) 1996 Academic Press Limited