Nature is disordered, messy and chaotic, but if we look closely, we may begin to notice patterns, order and symmetry at many scales, from the most magnificent spiral galaxy to the tiniest snail shell.

The Fibonacci sequence is a popular pattern that appears in many places. You’ve probably seen it before as a spiral graphic that appears overlaid on images of a human ear, a hurricane, a nautilus shell, etc. But how many examples of the Fibonacci sequence actually occur 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 values that precede it: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

It was born from the mind of a 13th-century Italian mathematician. Leonardo Pisanoor the Fibonacci sequence, which itself is derived from a mathematical problem: if you put a pair of newborn rabbits together, one male and one female, it takes them one month to reach breeding age.

Assuming the rabbit colony does not die out, the female rabbit will give birth to another pair of baby rabbits, a male and a female. When the female grows up, the cycle repeats. If this pattern continues, with each female rabbit giving birth to another pair of rabbits over the course of a month, how many pairs of rabbits will there be in a year?

The equation we get from this problem is Fₙ = Fₙ₋₁ + Fₙ₋₂, where Fₙ is nth The Fibonacci numbers in the above sequence.

But the Fibonacci sequence can be applied to a lot more than just numbers and biologically impossible situations. You may have heard of the Golden Spiral, a logarithmic spiral that is considered one of the most perfect and beautiful patterns.

If you draw a line through the middle of the spiral, you’ll see that with each iteration, it increases by a factor of 1.618. This number is the Golden Ratio, an irrational number obtained by dividing each Fibonacci number by the number before it. Artists, mathematicians, architects, and others have striven for this perfect ratio for thousands of years.

read more: Why is our universe filled with spirals?

## Examples of the Fibonacci Sequence in Nature

Given what we know about the Fibonacci sequence, how common is it in nature? Some scientists caution against applying the golden ratio or spiral to the natural world. Too AnywhereThis is not to say that the Fibonacci sequence does not exist, for fear of false myths being perpetuated by poorly sampled studies and pseudoscience.

### 1. Pine cones

(Credit: HighDispersion/Shutterstock)

If you pick up a pine cone from the ground, you will see two sets of spiral bracts that rotate out from the base where it was once attached to the tree. These spirals wrap around each other in opposite directions and come together at a specific angle of rotation.

By counting the bracts spiralling in opposite directions, you find a palm-sized example of the Fibonacci sequence occurring in nature, with each spiral usually taking on the adjacent Fibonacci number.

### 2. Sunflower

(Credit: Kate Babie/Shutterstock)

Sunflowers are another famous example of Fibonacci at work in nature. In particular, the arrangement of sunflower seeds often follows the Fibonacci sequence: while seeds in rows of 34, for example, curve clockwise, seeds in rows of 21 or 55 spiral in the opposite direction.

However, this is natural and random, so not all sunflowers will fit this pattern. The Fibonacci numbers are a common structure found in sunflower seeds, but A recent study evaluating data from over 600 community-grown sunflowers We found that some of the sequences were so random that they did not follow the Fibonacci sequence.

But scientists believe that by following the Fibonacci sequence in the first place, sunflowers are able to fit as many seeds as possible on their heads.

### 3. Tree Branches

(Credit: JND Photography/Shutterstock)

If you look up at trees, you will see that the points where the branches split off from the trunk are also likely to be related to the golden ratio. For example, in a poplar tree, Researchers model the golden ratio for plants The angle between the branches growing from the main trunk of the poplar is 34.4 degrees, which, when compared to a 90-degree angle, satisfies the golden ratio.

### 4. Plant leaves

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The arrangement of leaves around a plant’s stem, also known as phyllotaxis, is another area of biology where the Fibonacci sequence comes into play. Just as the Fibonacci sequence helps sunflowers pack the most seeds into their flowers, researchers believe that arranging leaves according to the Golden Ratio is also a way for plants to maximize their light-gathering ability and extend their lifespan.

### 5. Petals

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There are many other kinds of flowers, such as roses, buttercups, and lilies. Following the Fibonacci sequence Number of petals. For example, wild roses typically have five petals, which is early in the Fibonacci sequence. The number of petals, like leaves, also helps to maximise the amount of light a flower can absorb while it is growing.

### 6. The Human Body

(Credit: YummyBuum/Shutterstock)

Of course, the Fibonacci numbers are found not only in the world around us, but also in our own 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 continue to discover new ways in which these numbers appear. For example, Recent reviews for 2022 He discovered that the ratio between the distance from his navel to his feet and the distance from his navel to his head forms the golden ratio.

### 7. Whales

(Credit: Danita Delimont/Shutterstock)

Latest news from the beginning of the yearIssue 24 made headlines for whales’ ability to create Fibonacci spirals during their hunting process, with particular media attention being drawn to two enormous humpback whales spewing spiralling bubbles towards the ocean’s surface and casting bubble nets to capture their prey.

The net appeared on the surface of the ocean in a tightly wound spiral, a beautiful sight indeed to behold. Not necessarily a Fibonacci spiralIt depends on the specific proportions and ratios. Still, it’s a remarkable spiral, and another opportunity for scientists to gain a deeper understanding of the whales’ hunting habits.

### 8. Galaxy

(Credit: Triff/Shutterstock)

Stepping back a little from Earth and looking at our existence on the grandest scale of the universe, spiral galaxies strike us as just another example of nature’s golden spiral. But according to researchers in a paper published in the journal Nature in 2022, Symmetric He pointed out, Real galaxies are incomplete and chaoticIt does not necessarily correspond perfectly to the golden spiral or the golden ratio.

But that doesn’t mean Fibonacci patterns don’t exist in the universe at all: the article’s authors add that the average distances of the planets in our solar system to the sun “are roughly related to each other according to the golden ratio.”

### 9. Pineapple

(Credit: Zapylaieva Hanna/Shutterstock)

The pineapple is often cited as an example of the Fibonacci sequence in fruit because of the spiral pattern created by each bulb within the fruit. A 1978 study The pineapple spiral is made up of the Fibonacci sequence, but it turns out that the spiral doesn’t necessarily point in the same direction in every species of pineapple.

### 10. Nautilus Shell

(Credit: ZHMURCHAK/Shutterstock)

The nautilus shell has come a long way since it was celebrated as the manifestation of the Fibonacci sequence in seashells. It may resemble a golden spiral, The scientists then The idea is that these shells perfectly follow the golden ratio, with the ratio across the Nautilus genus actually being closer to 1.310 rather than 1.618.

read more: 5 Amazing Natural Phenomena That Are Too Amazing to Be Real

## Why does Fibonacci appear in nature?

Researchers have yet to arrive at a single, all-purpose theory of why nature favors symmetry and patterns. Living systems may appear symmetric because physical forces larger than the living systems themselves impose constraints on their functioning.

Or symmetry within the tiniest particles and molecules that make up everything could also play a role. It could be purely a matter of survival and evolutionary advantage, much like how plant leaves use the golden ratio to maximise the efficiency of photosynthesis.

Some researchers think we may never get to the reasons why: “A general unified theory of symmetry in biology does not exist and is probably never likely to be developed,” the authors conclude. Articles published in journals in 2022 Biophysica.

This is not to discount the importance and prevalence of patterns in a chaotic world, but you’ll find something out of place even in the most seemingly orderly of things, from sunflowers to galaxies.

read more: The Secret Science of Fairy Rings

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