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Fibonacci sequence optimizes packing: sunflowers


Helianthus annuus / Ethbaal / LicenseGFDL - Gnu Free Document License

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

"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 leavesThe 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)

"Phyllotactic patterns are established at a microscopic scale by a process known as meristematic development. For example, the patterns seen in large sunflower heads are actually established when the sunflower's blossom is only 2 mm in diameter. The botanical units or plant organs composing these patterns are formed in the small shoot apices of plants. They first appear at the usually circular edge of an apex (or apical meristem) as bulges of cells called primordia (see Figure 3). The biological mechanism of primordial formation is still unknown, although various hypotheses have been brought forward such as anisotropic concentrations of morphogens or inhibitory chemical substances (yet to be determined), or buckling of a layr of cells (tunica) over the core (corpus) of the apex." (Atela et al. 2003:642) From caption of Figure 3: "New primordia form as far away as possible from existing primordia. Once formed, primordia move radially away from the center of the apex." (Atela et al. 2003:643)
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Med_helianthus_whorl Helianthus

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Organism/taxonomy data provided by:
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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

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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Atela P; Golé C; Hotton S. 2003. A dynamical system for plant pattern formation: a rigorous analysis. Journal of Nonlinear Science. 12(6): 641-676.
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over 5 years ago
Here it is a project for solar panels (using Fibonacci sequence) by a 13 years old boy:
over 6 years ago
Here's an interesting article:
over 6 years ago
Here's a beautiful video called Nature by Numbers: A Short Movie Inspired by Numbers, Geometry and Nature by Cristobal Vila:
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