Phyllotaxis

In an opposite pattern, if successive leaf pairs are 90 degrees apart, this habit is called decussate.

Examples of trees with whorled phyllotaxis are Brabejum stellatifolium[4] and the related genus Macadamia.

[5] A whorl can occur as a basal structure where all the leaves are attached at the base of the shoot and the internodes are small or nonexistent.

A basal whorl with a large number of leaves spread out in a circle is called a rosette.

This gives rise to a self-propagating system that is ultimately controlled by the ebb and flow of auxin in different regions of the meristematic topography.

[11] In 1754, Charles Bonnet observed that the spiral phyllotaxis of plants were frequently expressed in both clockwise and counter-clockwise golden ratio series.

Since three golden arcs add up to slightly more than enough to wrap a circle, this guarantees that no two leaves ever follow the same radial line from center to edge.

Botanists are divided on whether the control of leaf migration depends on chemical gradients among the primordia or purely mechanical forces.

[citation needed] Physical models of phyllotaxis date back to Airy's experiment of packing hard spheres.

[15] Douady et al. showed that phyllotactic patterns emerge as self-organizing processes in dynamic systems.

[16] In 1991, Levitov proposed that lowest energy configurations of repulsive particles in cylindrical geometries reproduce the spirals of botanical phyllotaxis.

[18][19] They demonstrated that these interacting particles can access novel dynamical phenomena beyond what botany yields: a "dynamical phyllotaxis" family of non local topological solitons emerge in the nonlinear regime of these systems, as well as purely classical rotons and maxons in the spectrum of linear excitations.