PHYLLOTAXIS AS A DYNAMICAL SELF-ORGANIZING PROCESS .1. THE SPIRAL MODES RESULTING FROM TIME-PERIODIC ITERATIONS

This article is the first of a series of three in which the various ph yllotaxic modes are shown to result from successive iterations of two possible simple dynamical systems. In this first part the hypotheses p ut forward by Hofmeister (1868) for the formation of primordia are re- examined and shown to form the rules of such a system. By means of a p hysics experiment and a numerical simulation, it is demonstrated that this system gives rise to the self organization of the spiral phyllota ctic structures. The dynamic is controlled by only one parameter, G, e quivalent to Richards' plastochrone ratio (1951), which characterizes growth. The diagram representing the values of the divergence angle as a function of the plastochrone ratio resembles that obtained geometri cally by van Iterson (1907). In the present results, however, only one branch of solutions is continuous for all values of G; this differenc e with the geometrical results is important. The predominance of Fibon acci order in botany is related to this continuity: during the ontogen y, because of the continuous decrease in G, only this branch is follow ed. In this framework the build-up of such complex structures as the i nflorescence of compositae is described. (C) 1996 Academic Press Limit ed