Details

The term phyllotaxis refers to the arrangement of leaves, seeds or petals on a plant stem, which follows a spiral pattern that maximizes exposure to sunlight and minimizes shading of lower leaves. This fascinating pattern can be represented mathematically using a golden angle–based approach, creating a visually appealing and relatively well-distributed set of points on a sphere.

This Demonstration showcases these patterns in a three-dimensional space. Points are distributed uniformly on a sphere using the golden angle, which is derived from the golden ratio—an irrational number that holds great significance in art, architecture and mathematics. The golden angle ensures that each point is placed at an angle that minimizes overlap and optimizes spacing.

The phyllotaxis method not only offers a visually stunning point distribution but also provides valuable insights into the underlying principles governing the growth patterns of plants such as sunflowers, pinecones and succulents.

Reference

[1] J. Kogan, "A New Computationally Efficient Method for Spacing Points on a Sphere," Rose-Hulman Undergraduate Mathematics Journal, 18(2), 2017 Article 5. scholar.rose-hulman.edu/rhumj/vol18/iss2/5.