Phyllotaxis as a Dynamical Self Organizing Process Part I] The Spiral Modes Resulting from Time!Periodic Iterations

This article is the _rst of a series of three in which the various phyllotaxic modes are shown to result from successive iterations of two possible simple dynamical systems [ In this _rst part the hypotheses put forward by Hofmeister "0757 # for the formation of primordia are re!examined and shown to form the rules of such a system [ By means of a physics experiment and a numerical simulation \ it is demonstrated that this system gives rise to the self organization of the spiral phyllotactic structures[ The dynamic is controlled by only one parameter \ G \ equivalent to Richards | plastochrone ratio "0840#\ which characterizes growth [ The diagram representing the values of the divergence angle as a function of the plastochrone ratio resembles that obtained geometrically by van Iterson "0896# [ In the present results \ however \ only one branch of solutions is continuous for all values of G ^ this di}erence with the geometrical results is important [ The predominance of Fibonacci order in botany is related to this continuity] during the ontogeny \ because of the continuous decrease in G \ only this branch is followed[ In this framework the build!up of such complex structures as the in~orescence of compositae is described[ 7 0885 Academic Press Limited