Fibonacci Numbers, Phyllotaxis and a Bit of Philosophy

Phyllotaxis, the striking natural phenomenon of spiral patterns in plants, has long been a subject of scientific intrigue. Despite attracting attention from eminent mathematicians like Alan Turing, a complete explanation for the ubiquitous appearance of Fibonacci numbers in these patterns has remained elusive. This review paper suggests that previous failures to solve the “phyllotaxis riddle” stem from incorrect philosophical assumptions and a misinterpretation of causality, particularly concerning the “Hofmeister rule” and the role of auxin. The authors introduce a recursive biomechanical model that defines phyllotaxis morphogenesis as two simultaneous processes: the discrete emergence of new primordia at regular intervals and their continuous growth. This model, which posits that spiral structures are a natural consequence of mechanically balancing growth pressure and external environmental pressure, successfully generates both Fibonacci and Lucas patterns without pre-programmed mathematical sequences. The model’s validity is confirmed by systematically varying key parameters, revealing that the specific combination of growth rate and environmental pressure determines the resulting phyllotaxis type. The study concludes that spiral phyllotaxis morphogenesis occurs through simple mechanical interactions within classical physics frameworks, excluding the need for informational or “magical” forces.