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


“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)

Journal article
Sympodial Construction of Fibonacci-type Leaf Rosettes in Pinguicula moranensis (Lentibulariaceae)Annals of BotanyOctober 21, 2016
V. Grob, E. Pfeifer, R. Rutishauser

“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)

Journal article
A dynamical system for plant pattern formation: a rigorous analysis