Universality in Phyllotaxis: a Mechanical Theory

Abstract

One of humanity's earliest mathematical inquiries might have involved the geometric patterns in plants. The arrangement of leaves on a branch, seeds in a sunflower, and spines on a cactus exhibit repeated spirals, which appear with an intriguing regularity providing a simple demonstration of mathematically complex patterns. Surprisingly, the numbers of these spirals are pairs of Fibonacci numbers consecutive in the series 1, 2, 3, 5, 8, 13, 21, 34, 55... obeying a simple rule 1+2=3, 2+3=5, 5+8=13 and so on. This article describes how physics helps to clarify the origin of this fascinating behavior by linking it to the properties of deformable lattices growing and undergoing structural rearrangements under stress.