A synergic approach to plant pattern generation

The paper shows convergences between the results found in various models of phyllotaxis. It shows that a synergic approach is needed to deal with the problems of phyllotaxis. An algorithm, called the phi-model, based on the observation of the meaningful and symmetry-generating presence of the golden ratio phi in all types of spiral patterns, and consequently in all types of regular patterns in phyllotaxis, is proposed. The model is suggested by a property of the allometry-type model for pattern recognition in phyllotaxis. It extends recent morphological models developed around the idea of packing efficiency of plant primordia, models that yield the noble numbers, among which are the divergence angles of spiral patterns. The phi-model also gives the noble numbers and moreover orders them in a way that establishes connections with the morphogenetic principles used in models for pattern generation; the order has to do with the relative frequencies of the spiral patterns in nature. The phi-model is a link between the two entropy models in phyllotaxis and offers a nice correspondence with the minimal entropy model generated by a systemic and holistic approach. This latter type of approach is put forward as being able to give a general framework in which to organize the concepts, results, and models in phyllotaxis in a way that produces a synergy of efforts. The necessity of doing so is seen clearly when one considers that phyllotaxis-like patterns are encountered in other fields of research, so that the problem appears to transcend the strict botanical substratum.