It turns out that if a plant grows one leaf, then the next phi (the golden ratio) rotations from the first, then the third phi rotations from the second, and the fourth phi rotations from the third, and so on, that process will result in the longest possible time before the newest leaf is in the shadow of any existing leaf.
same problem.Īs this species evolves, the plants whose leaves are most often useful have an advantage and breed more. If the second leaf is opposite the first then that is good, but the third will be in shadow and useless. If it grows a second leaf in the shadow of the first then that leaf is useless. And there are places in the natural world were extreme irrationality is the most efficient solution to a problem, so by natural selection living systems tend toward that value where it works best.Ĭonsider a plant that has grown one leaf.
It turns out that the golden ratio is not only an irrational number.
