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.

本项公民科学研究针对向日葵（Helianthus annuus）花盘螺旋中的斐波那契结构（Fibonacci structure）出现情况进行评估。该现象存在多种相互竞争的生物数学解释，我们的核心前提为：观测到斐波那契结构与非斐波那契结构，均可为这类模型的验证提供有效信息。本次研究共采集了657株向日葵的相关数据。在可靠性最优的数据集子集内，我们共统计了768组顺时针或逆时针旋列数（parastichy numbers），其中565组为斐波那契数，另有67组符合预定义类型的斐波那契结构。此外，我们还发现了此前未在向日葵中报道过的更复杂斐波那契结构。本研究为现有文献中第三项、亦是规模最大的同类研究，同时也是首个具备明确且可独立核查的纳入与分析标准、且数据完全公开可获取的相关研究。据我们所知，本研究首次系统性报道了不具备斐波那契结构的向日葵花盘。其中部分花盘仅近似符合斐波那契结构，我们特别发现：数值为斐波那契数减1的旋列数，其出现频率显著高于斐波那契数加1的旋列数。本研究另一项意外发现为准规则花盘（quasi-regular heads）的存在，这类花盘无法确定任意一组旋列数的具体归属。