Abstract
This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower (Helianthus annuus) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci and non-Fibonacci structure is informative for challenging such models. We collected data on 657 sunflowers. In our most reliable data subset, we evaluated 768 clockwise or anticlockwise parastichy numbers of which 565 were Fibonacci numbers, and a further 67 had Fibonacci structure of a predefined type. We also found more complex Fibonacci structures not previously reported in sunflowers. This is the third, and largest, study in the literature, although the first with explicit and independently checkable inclusion and analysis criteria and fully accessible data. This study systematically reports for the first time, to the best of our knowledge, seedheads without Fibonacci structure. Some of these are approximately Fibonacci, and we found in particular that parastichy numbers equal to one less than a Fibonacci number were present significantly more often than those one more than a Fibonacci number. An unexpected further result of this study was the existence of quasi-regular heads, in which no parastichy number could be definitively assigned.
Highlights
Fibonacci structure can be found in hundreds of different species of plants [1]
In practice, it is only feasible to estimate these parastichy numbers through a subjective visual process, for which we developed a protocol given in the electronic supplementary material, this is informed by the mathematical theory of phyllotaxis [1]
The distribution of observed parastichy numbers is given in figure 2, with a clear indication of a dominance of Fibonacci structure: detailed breakdowns are given in table 1
Summary
Fibonacci structure can be found in hundreds of different species of plants [1]. This has led to a variety of competing conceptual and mathematical models that have been developed to explain this phenomenon. It is not the purpose of this paper to survey these: reviews can be found in [1,2,3,4], with more recent work including [5,6,7,8,9,10]. We focus on providing empirical data useful for differentiating them.
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