Today on the podcast I'm talking with Matthew Pennybacker , a mathematician who studies patterns in plants. In his most recent work, Pennybacker and his colleague Alan Newel have provided a mathematical description of the beautiful, swirling patterns that we see in sunflower heads. Image by Bohringer Notice that the spirals on the sunflower head go in two directions: clockwise and counterclockwise. The number of spirals going in either direction usually differs on a single flower, and the number of spirals certainly varies from flower to flower; BUT the spirals still follow a regular pattern*: the number of spirals are almost always variables from something called the Fibonacci sequence. The Fibonacci sequence starts with numbers 1 and 1, and then proceeds as such: each new number is the sum of the last two numbers. So the sequence goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Now why on earth would plants want to exhibit such a pattern in the way they organize t