The possible and the actual in phyllotaxis: Bridging the gap between empirical observations and iterative models

This article presents new methods for the geometrical analysis of phyllotactic patterns and their comparison with patterns produced by simple, discrete dynamical systems. We introduce the concept of ontogenetic graph as a parsimonious and mechanistically relevant representation of a pattern. The ontogenetic graph is extracted from the local geometry of the pattern and does not impose large-scale regularity on it as for the divergence angle and other classical descriptors. We exemplify our approach by analyzing the phyllotaxis of two asteraceae inflorescences in the light of a hard disk model. The simulated patterns offer a very good match to the observed patterns for over 150 iterations of the model.