Fibonacci in nature: A mesmerizing sequence with explanation

Fibonacci in nature - examples that make it easy to understand the pattern

Mathematics can be beautiful. If you don't believe me, let's look at the examples of the Fibonacci sequence in nature. You can see it almost everywhere - from wonderful flowers to human embryos, snails and pinecones. But what makes it so pleasing to our eyes, and why it appears in nature is still a mystery.

Fibonacci in nature - fractals

Source: / Maklay62; modified: Richárd Seres-Nagy; License: Pixabay License (Free for commercial use; No attribution required); License link:; Link:

The origins of the Fibonacci sequence are rather unlikely - the Italian mathematician Leonardo Pisano (Fibonacci himself) created a thought experience in which he was trying to figure out what would happen - more precisely, how many bunnies would born - if one would start to breed one founding pair of rabbits among optimal conditions.

He indicated that after a month, the oroginal pair of rabbits would remain, but none would be born yet, next on, a pair of new rabbits would be born, one of them a male, the other one a female. Next time, only the older pair would give birth to bunnies, as the other pair would still be immature, which means three pairs of bunnies. After that, the firstborn pair would also produce a litter, making it five pairs of rabbits. This creates an order that follows this pattern: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.

Those who are not really interested in rabbit breeding, but more in arts may consider another explanation: each number of the sequel is the sum of the previous two, and the ratio between the numbers is exactly that of a golden ratio (1.618034).

Where is the Fibonacci sequence found in nature?

The Fibonacci sequence is found in nature quite often, and even those who know nothing about it are usually amazed by the fantastic order and sight.

Fibonacci sequences on snail shell

Source: / juliaparrot; modified: Richárd Seres-Nagy; License: Pixabay License (Free for commercial use; No attribution required); License link:; Link:

Did you know for example that honey bee colonies, especially the family trees of the drones are also following a golden ratio pattern? You'll see that there is one queen, a small number of drones, and many workers. The queens have two parents, but the drones have only one, as they hatch from eggs that are not fertilized. This means a drone has one parent, two grandparents and three great-grandparents. And the pattern goes on like this.

One of the most outstanding examples of Fibonacci numbers in nature is the head and the flowers of the sunflower. If you count the small inner flowers that are arranged in a spiral form, you'll get a Fibonacci number, and if you divide these spirals into those that are pointed left and right, you'll also end up having two consecutive Fibonacci numbers. The same thing may apply to some other flowers, some pinecones and also in the case of the cauliflower.

What's also very interesting is that our DNA molecules also follow a Fibonacci sequence, as its 34 angstroms long and 21 angstroms wide per full cycles.

How does Fibonacci work in nature?

So how the Fibonacci sequel works in nature is usually interpreted into certain growing patterns. Even certain trees represent these numbers when they grow, and when you see the tail of a chameleon, it also has this kind of pattern. But as it's written on the blog of the University of Melbourne (The universe in a spiral - The University of Melbourne) even spiral galaxies - among them, the Milky Way - can be described with a golden ratio. But the question preveils - do the Fibonacci numbers have a reason or purpose that makes them so frequent, or is it just a coincidence

What is a real world example of the Fibonacci numbers?

But humans always found the golden ratio appealing to the eyes, even when they didn't yet know what was so fantastic about it - and once they knew, perhaps they were even more fond of it. The Lunette of San Nicola, Leonardo's Mona Lisa, The Pantheon, Hokusai's Great Wave and the Taj Mahal have at least one thing in common: a very strong golden ratio-based composition/structure that makes them so powerful, yet peaceful and stable at the same time.

But the golden ratio quire frequently appears in music as well - great composers, such as Beethoven also used golden ratio and Fibonacci sequels in their pieces, even if they did so naturally, and without knowing that they created such a mathematically interesting structure.

And guess what? Bonsai trees are also usually grown to form a golden ratio…!

Why is Fibonacci found in nature?

It's not yet known why Fibonacci numbers appear in nature this many times. While some say it's just a coincidence, there are times when it has practical benefits. For example, the flowers may grow this way to optimize the amount of sunshine that's available. Some scientists also say that it's the asymmetrical stem cell division that makes spiral growing patterns common.

So while the origins of certain, naturally appearing Fibonacci sequels might be different, they still have a certain benefit or reason - we just haven't yet noticed what it might be in some cases.

A. D.

March 21, 2021