One of the key rules of biology is that individuals attempt to produce as many offspring as possible. Thus, plants like sunflowers try to maximize their seed production by packing seeds into the flower head in the most optimal way. How is this archived?
Each disk flower [and therefore also each seed] is oriented toward the next by approximately the golden angle, 137.5°. This produces an intricate pattern of interwoven spirals with one set curving to the left, and another set curving to the right [see todays’s photograph]. Intriguingly, the numbers of spirals running clockwise and the numbers of spirals running anticlockwise are always adjacent members of the so-called ‘Fibonacci series’.
[Leonardo Fibonacci, a 13th-century mathematician, discovered a mathematical series in which each number is obtained simply by adding together the previous two numbers.]
Typically, there are 34 spirals in one direction and 55 in the other. On a very large sunflower there could be 89 in one direction and 144 in the other.
How do plants like sunflowers create such perfect disk flower arrangements?
A plant hormone called auxin, which spurs the growth of leaves, flowers, and other plant organs, is the key: Disk flowers grow where auxin flows. Using a mathematical model that describes how auxin and certain proteins interact to transport each other around inside plants, researchers could predict where the hormone would accumulate. Simulations of that model reproduced patterns exactly matching real ‘Fibonacci spirals’ in sunflowers. Based on their results, the researchers suggest that such patterns might be more universal in nature than previously thought.
[The study was published by Matthew Pennybacker and Alan C. Newell in Phys. Rev. Lett. 110, 248104.]