Phyllotaxis

Phyllotaxis is the study of the spatial arrangement of leaves on a plant stem, and more broadly the arrangement of other organs such as seeds in a head or petals in a flower. It covers leaf phyllotaxis, as well as the positioning of seeds, florets, or fruiting structures within inflorescences. Patterns are often categorized as alternate (one leaf per node), opposite (two leaves per node), and whorled (three or more leaves per node). A common and striking pattern is spiral phyllotaxis, where successive leaves are offset along the stem to produce two interlaced spirals.

The divergence angle, the angular offset between successive leaves, frequently clusters near the golden angle of about 137.5 degrees. This arrangement helps maximize light exposure for all leaves and can promote efficient packing of organs on a growing shoot. In many species the number of visible spirals corresponds to consecutive Fibonacci numbers (for example 5 and 8, or 8 and 13).

Phyllotactic patterns are explained by growth processes at the shoot apex: new primordia are initiated at roughly constant intervals, while the stem elongates, guiding later leaves outward in a way that can be modeled by mathematical forms such as Fermat's spiral or Vogel's model. Deviations occur due to genetic variation or environmental factors, yielding occasional non-Fibonacci or mixed patterns.

Phyllotaxis has applications in botany, horticulture, and biomimetic design, and provides insight into how plants optimize space, growth, and resource capture.