THE spiral patterns of growth seen in many plants, such as cacti and sunflowers, follow a precise mathematical sequence, but just why they do has always been a mystery. Now the problem has been solved: these patterns minimise the amount of mechanical stress in a growing plant.
The spirals are easy to spot. For example, a cactus head is full of bumps that each sport a pointed tip or “sticker”. In some cacti, you can start at the centre and draw spirals connecting each sticker to its nearest neighbour. What you get are three sets of spirals: one with three, another with five; and the third with eight members.
These are consecutive numbers in a mathematical sequence known as the Fibonacci series in which each number is the sum of the previous two. The series reads: 1, 1, 2, 3, 5, 8, 13, 21, and so on.
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“The question is: why do you see Fibonacci numbers of spirals,” says Patrick Shipman, a graduate student at the University of Arizona in Tucson.
Shipman wondered if the spirals had anything to do with mechanical stress in the growing plant. The tip of the plant shoot is the active region of growth. It is covered by a thin outer layer called the tunica, which is connected to the mass of softer cells inside. As the plant grows, the tunica hardens and then buckles under the mechanical stress caused by further growth.
This buckling is important because local variations in stress form regions called primordia which give rise to leaves – or their counterparts in cacti, the stickers. As the growing tip puts out new plant material, new primordia appear.
Shipman and his adviser, Alan Newell, have developed a mathematical model to look at the mechanical stresses in the tunica. In a cactus for instance, the tunica deforms in a way that creates sets of ridges on its surface.
The number of ridges in each set follows a Fibonacci series which according to Shipman and Newell is exactly the pattern predicted by their mathematical model to minimise the stress in the tunica (Physical Review Letters, DOI: 10.1103/PhysRevLitt.92.168102). Stickers form where the ridges intersect, which is why they are also related to the Fibonacci sequence.