A History of Phyllotaxis Research

Ancient Greek naturalists, notably Theophrastus, documented various types of leaf arrangement: opposite, whorled, and alternate (spiral). His records laid the foundation for later attempts to understand the geometry of leaf spirals.

Source: Enquiry into Plants

During the Renaissance, Leonardo da Vinci observed spiral patterns in leaves and plant organs. Though he didn't formalize these mathematically, his notes reflected growing curiosity about natural patterns.

Source: Codex Atlanticus (Digital Edition)

Swiss naturalist Charles Bonnet introduced the term phyllotaxis in his 1754 treatise Recherches sur l'usage des feuilles dans les plantes. He observed that leaf spirals often correspond to pairs of Fibonacci numbers and highlighted the approximate divergence angle of 137.5°, linking it to the golden ratio in nature.

Source: Recherches sur l'usage des feuilles...

German botanist Karl Friedrich Schimper introduced the concept of the genetic spiral and divergence angle (~137.5°) and coined the term parastichy. He identified visible spiral families and observed Fibonacci pair numbers in leaf spiral counts.

Source: Symphytum Zeyheri (1835 reprint)

Alexander Braun expanded on Schimper's ideas, visualizing transitions between phyllotactic fractions. He analyzed fir-cone scale arrangements and confirmed that many plants exhibit leaves in fractions like 2/5, 3/8, 5/13, corresponding to consecutive Fibonacci ratios.

Source: Vergleichende Untersuchung...

French brothers Auguste and Louis Bravais described leaf arrangement as a lattice on a cylinder. They showed that visible spiral rows (parastichies) follow Fibonacci number sequences. Their mathematical model established the connection between phyllotaxis and crystallography.

Source: Ann. Sci. Nat. ser.2 vol.7

Wilhelm Hofmeister proposed that each new leaf primordium emerges at the location with the most space, as far as possible from existing ones. This leads to a consistent divergence angle near 137.5°, giving rise to Fibonacci spirals.

Source: Allgemeine Morphologie... (1868)

Simon Schwendener proposed a mechanical theory where primordia act as elastic bodies, organizing under contact pressure. This model explained spiral rows through mechanical interaction, offering an alternative to purely geometric interpretations.

Source: Mechanische Theorie der Blattstellungen (1878)

A. H. Church summarized phyllotaxis in On the Relation of Phyllotaxis to Mechanical Laws (1904). He emphasized lattice models on cylinders and illustrated transitions between arrangements, mathematically formalizing the concepts of orthostichies, parastichies, and divergence angles.

Source: On the Relation of Phyllotaxis to Mechanical Laws

The Snows used microsurgical experiments to demonstrate that primordia suppress nearby organ formation. In 1962, they proposed a diffusion-based inhibition model, supporting Hofmeister's rule. Their work connected geometric theories with biological mechanisms.

Source: Phil. Trans. Royal Soc. B 244: 483 (1962)

Stéphane Douady and Yves Couder recreated phyllotaxis in vitro using liquid drops and floating magnetic particles. The same Fibonacci spiral patterns emerged purely from physical self-organization, without any biological cells.

Source: Phys. Rev. Lett. 68 (1992): 2098

Reinhardt and colleagues showed that auxin and its transport protein PIN1 are essential for organ initiation. Auxin accumulates at sites where new primordia will form, and disrupting auxin transport abolishes phyllotaxis.

Source: Nature 426: 255 (2003)

Takaaki Yonekura and Munetaka Sugiyama developed a new mathematical model where each primordium exerts not only inhibitory effects but also an inductive effect on the formation of the next organ. This reproduced the steep spiral and one-sided leaf rows seen in certain tropical plants.

Source: J. Plant Res. 137: 143 (2024)