In 1868 botanist Wilhelm Hofmeister hypothesized that, at the tip of a plant's shoot, new leaves form in regular time intervals (the plastochrone) and in the position where previously formed leaves leave the largest available space.
Based on this, Douady and Couder (1996) developed a mathematical model able to reproduce patterns often observed in nature such as the eventual constancy of the divergence angle drawn by two successive leaves, its relation to the golden angle, and the appearance of the Fibonacci numbers in spiral patterns generated by the spatial configuration of leaves.
This 2D model, describing processes on the shoot's surface, generalized straightforwardly to other dimensions. We simulated the three-dimensional case. The generalized divergence angles show unexpected patterns of convergence (as in 2D), but additionally periodicity as well as chaos.

Phyllotaxis, Dynamical Systems, Packing Efficiency