Nature is chaotic, messy, and chaotic. But if you look closely, you can begin to notice patterns, sequences, and symmetries on all sorts of different scales, from the largest spiral galaxy to the smallest snail shell.
One of the popular patterns found in many places is the Fibonacci sequence. You’ve probably seen it before, perhaps as a spiral graphic often superimposed on images of a human ear, a hurricane, or a nautilus shell. How many of these are examples of the Fibonacci sequence occurring in nature?
What is the Fibonacci sequence?
Simply put, the Fibonacci sequence describes a series of numbers, where each successive value is the sum of the two previous values: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.
It came from the mind of a 13th century Italian mathematician. Leonardo PisanoOr Fibonacci. This sequence itself is derived from a mathematical problem. Let’s say that if you put a pair of newborn rabbits (one male and one female) together, it takes them a month to reach the age where they can reproduce.
Assuming that the population never decreases, the female rabbit will produce another pair of male and female rabbits. When those females grow up, they will do the same. If this pattern continues, and it takes each female rabbit a month to produce another pair, how many pairs of rabbits will there be in a year?
The formula for this problem is Fₙ = Fₙ₋₁ + Fₙ₋₂, where Fₙ is nth The above sequence is the Fibonacci sequence.
But the Fibonacci sequence has many applications beyond numbers and biological impossibilities. You may have heard of the golden spiral. The logarithmic spiral is considered one of the most perfect and beautiful patterns you can achieve.
If you draw a line along the center of the spiral, you will see that it increases by 1.618 times with each repetition. This number is the golden ratio, which is an irrational number that is obtained by dividing a Fibonacci number by the previous number. Artists, mathematicians, and architects have all aspired to this perfect ratio for thousands of years.
Read more: Why is our universe full of spirals?
Examples of the Fibonacci sequence in nature
Given what we know about the Fibonacci sequence, how common is it in nature? Some scientists warn against attributing it to the golden ratio or spiral. ~ too everywhereFor fear of perpetuating false myths with poorly sampled studies or pseudoscience. At the same time, this does not mean that the Fibonacci sequence does not exist at all.
1. Pine cone
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If you pick up a pine cone from the ground, you will see two sets of spiral bracts, which rotate out from the base where they were once attached to the tree. These spirals wrap around each other in opposite directions, and are positioned relative to each other at a specific angle of rotation.
You can see a palm-sized example of nature’s Fibonacci numbers popping up by counting the bracts arranged in opposite spirals, each spiral generally following the adjacent Fibonacci number.
2. Sunflower
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Sunflowers are another famous example of the Fibonacci sequence at work in nature. In particular, the arrangement of the seed heads in sunflowers often follows the Fibonacci sequence. For example, if a row of 34 seeds spirals clockwise, a row of 21 or 55 seeds spirals in the opposite direction.
However, since this is nature and random things happen, not all sunflowers follow this pattern. Fibonacci numbers are the general structure of sunflower seeds, but A recent study evaluated data from over 600 citizen-grown sunflowers. We found that some of them were so disordered that they did not follow the Fibonacci sequence.
However, scientists believe that following the Fibonacci sequence allows sunflowers to fit as many seeds on their heads as possible.
3. Tree branches
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If you look up at a tree canopy, the points where branches branch off from the original trunk are likely to be related to the golden ratio. For example, in the case of a poplar tree, Researchers Model the Golden Ratio in Plants They found that the angle between the branches of a poplar growing from the main trunk was 34.4 degrees, which is equivalent to a 90-degree angle and therefore satisfies the golden ratio.
4. Plant leaves
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The arrangement of leaves around a plant stem, or phyllotaxy, is another area of biology where the Fibonacci sequence shines. Just as sunflowers are able to pack as many seeds into their heads as possible thanks to the Fibonacci sequence, researchers believe that the arrangement of leaves according to the golden ratio is how plants maximize their light-gathering potential, thus increasing their longevity.
5. Petals
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There are many different types of flowers, from roses to watercress and lilies. Follow the Fibonacci numbers In the petals. For example, wild roses usually have five petals, which is one of the first numbers in the Fibonacci sequence. The number of petals, like the leaves, allows the flower to maximize the amount of light it can absorb while growing.
6. Human body
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Of course, Fibonacci numbers are not only found in the world around us, but also in our bodies. The role of the golden ratio in the ideal human body has long been studied since the time of artists such as Leonardo da Vinci.
Even today, scientists are still finding new ways in which the numbers appear. For example, Recent Reviews 2022 It was discovered that the ratio of the distance from the navel to the feet and the distance from the navel to the head forms the golden ratio.
7. Whale
(Source: Danita Delimont/Shutterstock)
Latest news from early February024 has sparked a buzz about whales’ ability to create Fibonacci spirals while hunting. One that has caught the media’s attention in particular is a pair of large humpback whales who blow bubbles into the ocean’s surface in a spiral shape to cast a net of bubbles to catch their prey.
The net appeared as a tightly coiled spiral on the sea surface, and it was certainly a beautiful sight for onlookers. But it was not. It’s definitely a Fibonacci spiralIt depends on certain ratios and proportions. Still, it was an amazing spiral and another opportunity for scientists to better understand the whales’ hunting habits.
8. Galaxy
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When we step away from Earth for a moment and look at our existence on the grandest cosmic scale, spiral galaxies are another natural example of golden spirals that come to mind. But as the researchers in an article published in the journal Astronomy and Astrophysics in 2022 put it: symmetry I noticed, Real galaxies are imperfect and disorderedAnd it doesn’t always match perfectly with the golden spiral and ratio.
But that doesn’t mean Fibonacci patterns don’t exist in our universe at all. The authors of the article added that the average distances between the planets in our solar system and the Sun are “roughly related to each other according to the golden ratio.”
9. Pineapple
(Credit: Zapylaieva Hanna/Shutterstock)
Pineapples are often cited as an example of the Fibonacci sequence in fruits, thanks to the spiral pattern that each cluster within the pineapple fruit creates. A study from 1978 The pineapple spiral is composed of the Fibonacci sequence, but we found that the spiral does not always follow the same direction across all pineapple species.
10. Nautilus clam
(Source: ZHMURCHAK/Shutterstock)
The Nautilus shell has come a long way since it was first praised for its representation of the Fibonacci sequence in its shell. It may resemble the golden spiral, but Scientists have since refuted this. The idea that these shells perfectly follow the golden ratio. This ratio is actually closer to 1.310 than 1.618 for the entire Nautilus genus.
Read more: 5 Amazing Natural Phenomena That Don’t Seems Real
Why does Fibonacci appear in nature?
Researchers have yet to stumble upon a single theory that applies to all cases as to why nature seems to favor symmetry and patterns. Biological systems may appear symmetrical because physical forces greater than themselves impose constraints on how they operate.
Or perhaps the symmetries within the smallest particles and molecules that make up everything else also play a role. It could be a matter of pure survival and evolutionary advantage, like how plant leaves utilize the golden ratio to maximize efficiency in photosynthesis.
Some researchers believe we may never discover the reason by accident. “There is no general unified theory of symmetry in biology and it is unlikely that one will ever be developed,” the authors conclude. Article published in the journal in 2022 Biophysics.
That’s not to say we ignore the importance or popularity of patterns in a chaotic world, but even in the most seemingly organized things, from sunflowers to galaxies, you’ll find something that seems out of place.
Read more: The Secret Science of Fairy Circles
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