Phyllotaxis and Fibonacci
This post will attempt to explain a strange phenomenon in nature. If you look into a sunflower, daisy, cactus or fir cone you always see a spiral pattern like the one shown above. If you look carefully you in fact see two: one spiralling clockwise and the other spiralling anti-clockwise. And, bizarrely, if you count the number of spiral arms of each you always find they form a consecutive pair from the Fibonacci sequence. To recap, the Fibonacci sequence is the sequence you get if you start off with $F_1 =1$ and $F_2 = 1$ and then iterate using $F_{n+2} = F_{n+1}+F_n$. So: $$ (F_n) = 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,... $$ This all seems highly contrived, but somehow turns up in seed and leaf patterns. How? The answer has to do with Phyllotaxis. This is the manner in which new leaves or seeds are formed. Imagine a long stem plant growing upwards and generating new leaves as it grows. The tip of the plant is known as the bud ...