Data from: Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment

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.

本公民科学项目旨在探究向日葵（Helianthus annuus）花盘螺旋结构中的斐波那契结构（Fibonacci structure）出现情况。该现象存在多种相互竞争的生物数学解释，本研究的核心前提为：观测到斐波那契结构与非斐波那契结构，均可为驳斥此类模型提供有效依据。我们共收集了657株向日葵的相关数据。在可靠性最高的数据集子集中，我们对768组顺时针或逆时针方向的傍线数（parastichy number）进行了分析，其中565组为斐波那契数，另有67组属于预先定义类型的斐波那契结构。我们还发现了此前在向日葵中未曾报道过的更为复杂的斐波那契结构。本研究为文献记载中第三项、也是规模最大的相关研究，同时是首个采用明确且可独立核查的纳入标准与分析准则、并公开完整数据集的同类研究。据我们所知，本研究首次系统性地报道了不存在斐波那契结构的向日葵花盘。其中部分花盘的结构近似斐波那契结构；我们特别发现，数值比斐波那契数小1的傍线数，其出现频率显著高于比斐波那契数大1的傍线数。本研究的另一项意外发现为存在准正则花盘（quasi-regular head）——此类花盘中无法明确判定任何傍线数。