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.

本公民科学研究项目针对向日葵（Helianthus annuus）花盘螺旋结构中的斐波那契结构（Fibonacci structure）出现情况展开评估。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：对斐波那契结构与非斐波那契结构的观测，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。在本研究最可靠的数据集子集中，共统计了768组顺时针或逆时针螺旋线数（parastichy numbers），其中565组为斐波那契数，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被报道过的更为复杂的斐波那契结构。本研究是现有文献中第三项、也是规模最大的同类研究，同时更是首个采用明确且可独立核验的纳入标准与分析准则，并公开全部原始数据的相关研究。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。其中部分花盘近似符合斐波那契结构；尤为关键的是，我们发现螺旋线数等于斐波那契数减1的情况，显著多于螺旋线数等于斐波那契数加1的情况。本研究还得到一项意外发现：存在一类准规则花盘，无法为其明确指定螺旋线数。