Phyllotaxis as a dynamical self organizing process .2. The spontaneous formation of a periodicity and the coexistence of spiral and whorled patterns

The conditions for the appearance of a new primordium put forward by Snow & 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 ideas about the possible nature of the interaction between primordia. By numerical simulation, it is demonstrated that this system is sufficient to spontaneously generate time periodic regimes in which the successive elements are organized either in Fibonacci spiral or in whorled modes of growth. We show that the dynamical system generally selects the pattern with the densest packing. The effect of the geometrical shape of the apex and of the primorida on the stability of the opposite decussate phyllotaxy is pointed out. (C) 1996 Academic Press Limited