Fibonacci sequence optimizes packing: sunflowers

1 of 6 Helianthus annuus / Ethbaal / License

The seed heads of sunflowers optimize the packing of seeds by arranging them in spirals of Fibonacci numbers.

Biomimicry Taxonomy

	Modify >
	Adapt/optimize >
	Optimize space/materials

Biomimetic Application Ideas

Optimal space use in buildings, urban planning, machinery, etc. Solar panel arrays Maximizing passive solar gain in buildings

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[Collapse all sections] Summary

"Patterning seeds in spirals of Fibonacci numbers allows for the maximum number of seeds on a seed head, packed uniformly, with no crowding at the center and no 'bald patches' at the edges. In other words, the sunflower has found optimal space utilization for its seed head. The Fibonacci sequence works so well for the sunflower because of one key characteristic—growth. On a sunflower seed head, the individual seeds grow and the center of the seed head continues to add new seeds, pushing those at the periphery outwards. Following the Fibonacci sequence ensures growth on the same terms indefinitely. That is to say, as a seed head grows, seeds will always be packed uniformly, and with maximum compactness." (Courtesy of the Biomimicry Guild)

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"The leaf rosettes of the carnivorous Pinguicula moranensis follow a spiral phyllotaxis approaching a Fibonacci pattern while the stalked flowers arise from extra-axillary sites between the leaves…The leaves of consecutive articles of such sympodially constructed rosettes are arranged along a spiral Fibonacci pattern (with divergence angles around 137°)…Sympodial construction of flowering shoots and leaf rosettes is also known from Aloe, Gunnera and Philodendron." (Grob et al. 2007:857)

About the inspiring organism

Helianthus
Helianthus

Organism/taxonomy data provided by:
Species 2000 & ITIS Catalogue of Life: 2008 Annual Checklist

Bioinspired products and application ideas

Application Ideas: Optimal space use in buildings, urban planning, machinery, etc. Array of solar panels to capture maximum amount of sunshine while reducing overall area used by panels. Arrangement of buildings to maximize area exposed for passive solar gain.

Industrial Sector(s) interested in this strategy: Packaging, building, engineering, energy

Concentrated solar plant - Solar power array

References

Grob V; Pfeifer E; Rutishauser R. 2007. Sympodial construction of Fibonacci-type leaf rosettes in Pinguicula moranensis (Lentibulariaceae). Annals of Botany. 100(4): 857-863.

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Comments

Here it is a project for solar panels (using Fibonacci sequence) by a 13 years old boy: http://www.a...

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