Phyllotaxis of Plant Shoots
At the shoot tip of a plant, a new leaf grows at a fixed angle from the previous leaf, which is very frequently the golden angle 137.5°. As the plant grows, the leaves are arranged in a pattern characterized by a common fraction. This Demonstration shows you how the phyllotaxis pattern changes and what patterns would be obtained if the plant used a different angle. The golden angle is the most advantageous angle, since the plant experiences the least change and is most likely to survive.
 T. Okabe, "Physical Phenomenology of Phyllotaxis," Journal of Theoretical Biology, 280(1), 2011 pp. 63–75. doi:10.1016/j.jtbi.2011.03.037.