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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2016
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4892450/ https://www.ncbi.nlm.nih.gov/pubmed/27293788 http://dx.doi.org/10.1098/rsos.160091 |
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author | Swinton, Jonathan Ochu, Erinma |
author_facet | Swinton, Jonathan Ochu, Erinma |
author_sort | Swinton, Jonathan |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-4892450 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-48924502016-06-10 Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment Swinton, Jonathan Ochu, Erinma R Soc Open Sci Biology (Whole Organism) 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. The Royal Society 2016-05-18 /pmc/articles/PMC4892450/ /pubmed/27293788 http://dx.doi.org/10.1098/rsos.160091 Text en http://creativecommons.org/licenses/by/4.0/ © 2016 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Biology (Whole Organism) Swinton, Jonathan Ochu, Erinma Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment |
title | Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment |
title_full | Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment |
title_fullStr | Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment |
title_full_unstemmed | Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment |
title_short | Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment |
title_sort | novel fibonacci and non-fibonacci structure in the sunflower: results of a citizen science experiment |
topic | Biology (Whole Organism) |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4892450/ https://www.ncbi.nlm.nih.gov/pubmed/27293788 http://dx.doi.org/10.1098/rsos.160091 |
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