'Plants embody math — they are little calculators, producing Fibonacci sequences'

Christophe Golé is Professor of Mathematical Sciences at Smith College and co-author of ‘Do Plants Know Math?’ Speaking to Srijana Mitra Das at Times Evoke , he discusses plants — and their number games:

What is the core of your research?

It is around phyllotaxis — this has roots in the Greek word ‘phyllo’ which means ‘leaves’ and ‘taxis’ meaning ‘order’. This is the ordering of leaves and by extension, any organ around the stem of a plant. These usually form a sort of spiral lattice, with theoretical properties that have been puzzling people for centuries, from Leonardo da Vinci to Johannes Kepler and Charles Darwin.

What is the Fibonacci phenomenon you study in plants?

I mentioned the spirals leaves and other organs form — think now of a pineapple, pinecones or sunflowers. They all have certain packed organ structures, be it seeds or scales, which form a very regular arrangement of spirals — these can be two intersecting sets, going in opposite directions. If you count these spirals, very often, you’ll find those numbers are two successive Fibonacci numbers — these are numbers you get recursively, starting with 1 and 1. Then, you add those two and you get 2. Then you add the last two or 1 and 2 — you get 3. Again, you add the last two or 2 and 3 — you get 5. You add 3 and 5 and get 8. You add 5 and 8 and get 13 and so on.
Plants show Fibonacci numbers going upto 233 in sunflowers. It’s a very striking phenomenon — Alan Turing wrote computer programs seeking to understand this.

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Why does this Fibonacci sequence occur in plants?

Scientists are figuring out whether this is an optimisation of resources. What we know for certain is the root mechanism that generates these patterns is somewhat of local optimal packing — a new organ occurs where there is the most space left by others. In 1868, Werner Hoffmeister, a botanist, discovered this. It was confirmed later by biochemistry and biomechanics. This seems like a local phenomenon which has global repercussions on the structure of a plant that take place microscopically. Some biologists argue this could be plants trying to maximise their exposure to the sun while others state — and I quite like this idea — this helps plants pack many organs onto a small bud. If a plant wants to protect its early organs, it’s easier if you pack more into a small area.
Consider the Romanesco broccoli — this exhibits both spirals and a fractal structure, its florets splitting into baby florets which themselves split more and more. This is a wonderful example of math in the plant kingdom. There are also many plant organs which don’t show Fibonacci structures — corn is an example. These have spirals but those are not organised in Fibonacci sequences. Instead, these are often close to one another — instead of having 8-13, for instance, you’ll have 6-7 or 7-8.

We’ve been using a dynamical model which thinks about these new organs like disks on a cylinder or cone — you pile these in the smallest possible place and you can observe most of the patterns occurring in plants. Interestingly, decreasing the radius of these disks has the same effect as enlarging the tip of the plant where the structure is born — so, if you imagine a strawberry plant, a few leaves emerge and suddenly, there is an explosion of fruit. The advantage of having this sequence could be the plant saying, ‘Ok, I’m going all out for reproduction now.’ The change of parameter is crucial in these structures.

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So, do plants know math — and how to use this?
In a sense, plants embody math — they are constantly doing this. Plants actually are little geometrically calculating machines, small calculators which create these structures and have done this for millions of years. Evidence shows us early plants weren’t Fibonacci but quasisymmetric though — so, clearly, plants have evolved to do this.


Climate change is causing huge shifts among plants now — is the Fibonacci sequencing likely to change?
We have circumstantial evidence of changed phyllotaxis in stressed plants. My colleague, Stephane Douady, once collected a bunch of The red world is fascinating pinecones from a particular tree — these were around 95% Fibonacci. Next year, they were much less so. A farmer told him someone had cut some branches of the tree — that would have changed the tree’s parameter, causing stress and altering the phyllotaxis. Climate change could induce similar stress — this needs more research.

Image credit: iStock

Do plants respond to change, using math, biology, physics and chemistry?
There is growing evidence that plants have far more developed sensory systems than thought earlier — those systems work at many levels, from biochemical to physical. There is evidence that trees can hear sounds in some capacity and scientists find one part of a plant can sense what’s happening in another part. Plants adjust very fast to their environment and change structure — plants that love light can evolve within one generation to those which sustain shade. They are extremely adaptive but some are perishing now under great pressure.

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