Parastichies

Parastichies are spiral lines that pass through successive elements of a plant’s arrangement, such as leaves, seeds, or scales, revealing one or more visible spirals on the stem or inflorescence. They are a feature of phyllotaxis, the study of how botanical organs are arranged around a axis.

These spirals arise from the way new elements are produced at a fixed angular offset from the previous ones, typically close to the golden angle of about 137.5 degrees, and at regular radial intervals. The result is a lattice-like pattern on a circular cross-section that supports several families of spirals. Each family is characterized by a step size that traces a spiral across the plant’s surface.

Parastichy numbers describe the counts of these prominent spiral families. Usually two coprime integers are given, often consecutive Fibonacci numbers, such as 21 and 34 or 34 and 55, which correspond to the two most visible parastichies. While Fibonacci pairs are common, non-Fibonacci parastichies can occur when growth deviates from the ideal angle or spacing.

In practice, parastichies help optimize packing of leaves and seeds, contributing to efficient exposure to light and space use. Their study intersects botany and mathematics, illustrating how simple growth rules yield complex, naturally occurring spirals. Related concepts include phyllotaxis, the golden angle, and Fibonacci-number patterns observed in plants.