Phyllotaxis

Phyllotaxis describes how plant organs are positioned relative to one another and to an axis. In an alternate arrangement, a single leaf forms at each node, with successive leaves appearing at different positions around the stem. Opposite leaves occur as pairs at a node, while whorled arrangements place three or more leaves at one level. Spiral patterns are especially noticeable in buds, cones and compact flower heads. These categories are useful in plant description and identification, although arrangement can vary with a plant's growth stage and some apparent whorls result from closely spaced nodes.

In many spiral patterns, families of visible spirals wind in opposite directions, and their counts often belong to the Fibonacci sequence: each number is the sum of the two preceding numbers. This is a frequent pattern, not a rule that every plant or every flower head must obey. At the shoot tip, successive leaf primordia in many plants are separated by an angle near 137.5 degrees, called the golden angle. As stems elongate, the arrangement observed on the mature stem can be expressed by simple fractions that approximate this angle; consequently, visible rows and spiral counts need not be identical at different stages of growth.

New aerial organs arise from the shoot apical meristem, a region of growing tissue at the tip of a shoot. Research identifies the plant hormone auxin as an important part of this process. Auxin transport and local production help create changing concentrations across the meristem, and cells in regions with suitable signals can begin forming a new primordium. The developing primordia and surrounding tissue influence where subsequent organs form. This provides a biological framework for studying phyllotactic patterns, but no single simplified explanation captures every species or all transitions in leaf arrangement.

Phyllotaxis is studied by botanists, developmental biologists and mathematicians because a small number of repeated developmental rules can produce conspicuous geometry. Patterns may change as a shoot grows, and the arrangement of external organs is related to internal structures such as vascular connections. Proposed models examine spacing, growth, transport of developmental signals and the costs of transitions between patterns. Such models offer explanations for particular observations; hypotheses about why Fibonacci-like patterns evolved should be distinguished from direct observations of leaf positions and from established roles of auxin in meristem development.