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 these models. We collected data on 657 sunflowers. In our most reliable data subset we evaluated 768 clockwise or counter-clockwise 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 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.本公民科学研究旨在探究向日葵（Helianthus annuus）花盘螺旋结构中的斐波那契结构（Fibonacci structure）存在情况。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：无论是观测到斐波那契结构还是非斐波那契结构，均对验证、驳斥相关模型具有重要参考价值。本次研究共收集了657株向日葵的相关数据。在最可靠的子数据集内，我们共统计了768组顺时针或逆时针副螺线数（parastichy number），其中565组符合斐波那契数列，另有67组属于预定义类型的斐波那契结构。此外，我们还发现了此前在向日葵中未曾报道的更为复杂的斐波那契结构。本研究为该领域第三项、亦是规模最大的学术研究，同时也是首个采用明确且可独立核查的纳入标准与分析准则，并公开完整可获取数据集的相关研究。本研究首次系统性报道了不存在斐波那契结构的向日葵花盘样本，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一的副螺线数，其出现频率显著高于数值为斐波那契数加一的副螺线数。本研究还有一项意外发现：存在一类准规则花盘，其副螺线数无法被明确界定。