Figure 2.
Modeled positions of auxin-supported wave collisions in the generative circle for three spiral phyllotaxes. For compact display of successive positioning of primordial initials, the radially outward movement of expanding primordia is not indicated, and all the plastochrons of one phyllotaxic repeat unit are shown in projection. That is, objects in planes at different z values are projected on an xy plane. (A–C) Waves propagate azimuthally from initially forming primordia (red bullets; colors guide the eye but the labels suffice to identify time points) in the clockwise and counterclockwise directions as indicated by “outward”-directed arrows at zero times. The wave fronts meet at sites that specify new primordium positions, as indicated by orange bullets with “inward”-directed arrows at t = τ. The meeting of the waves at time τ is not per se the immediate cause of primordium initiation; rather it is the buildup of auxin concentration that occurs at the sites in the interval between times τ and τ + T2. A new primordium emerges later in the plastochron T >>τ + T2. Waves generated anew at the orange bullets repeat the process. In B and C they collide at the green bullets; and in C successive rainbow colored bullets with sequential time labels indicate how the process repeats to complete a turn. The clockwise and counterclockwise waves AF,i+1 and BB,i+1 are given in equations (A.1) and (A.2) respectively.