Chapter 8: Implications for Everyday Systems

Section 6: Growth of Plants and Animals

History of phyllotaxis

The regularities of phyllotaxis were presumably noticed in antiquity, and were certainly recognized in the 1400s, notably by Leonardo da Vinci. By the 1800s various mathematical features of phyllotaxis were known, and in 1837 Louis and Auguste Bravais identified the presence of a golden ratio angle. In 1868 Wilhelm Hofmeister proposed that new elements form in the largest gap left by previous elements. And in 1913 Johannes Schoute argued that diffusion of a chemical creates fields of inhibition around new elements—a model in outline equivalent to mine. In the past century features of phyllotaxis have been rediscovered surprisingly many times, with work being done quite independently both in abstract mathematical settings, and in the context of specific models (most of which are ultimately very similar). One development in the 1990s is the generation of phyllotaxis-like patterns in superconductors, ferrofluids and other physical systems.

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From Stephen Wolfram: A New Kind of Science [citation]