The Fibonacci Sequence in Nature

fibronacci in nature

The fibonacci spiral appears not only in the perfect nautilus shell…  (image)

fibronacci in nature
…but in events and objects viewed from afar.

An energy system in the shape of a fibonacci moves with limited losses. Hurricane Irene.
fibronacci universe

What is the Fibonacci Sequence?

fibronacci spiral
The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is a recursive sequence,  generated by adding the two previous numbers in the sequence.: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…

Here is a good video explanation from SciShow. He points out that plant sections, petals, and rows of seeds almost always count up to a Fibonacci number.

fibonacci spiral
If you were to draw a line starting in the right bottom corner of a golden rectangle within the first square, and then touch each succeeding multiple square’s outside corners, you would create a fibonacci spiral.

How Common Is The Fibonacci Sequence in Nature?

fibronacci in nature
The fibonacci appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner. Here, a microscopic view of the ovary of an Anglerfish. Nikon’s It’s a Small World Competition.

Spirals are the most common galaxy shape. Galaxies group together in superclusters and superclusters group together in walls. These walls or filaments of numerous superclusters, gravitationally-bound and separated by large areas of void, are the largest known structures in the universe.

The Milky Way’s dust obstructs us from seeing the depth of these filaments or sheets, so we do not yet know the exact shape of these walls.

Cancer cell division. This composite confocal micrograph uses time-lapse microscopy to show a cancer cell (HeLa) undergoing cell division (mitosis). The DNA is shown in red, and the cell membrane is shown in cyan. The round cell in the centre has a diameter of 20 microns. Credit Kuan-Chung Su, LRI,

This is part 1 of three-part video series from “recreational mathematician” Vi Hart, explaining the mathematics behind the Fibonacci Sequence. Part 1 shows how you can draw the sequence and shows how it actually on pinecones and pineapples.

Amazing Examples of the Fibonacci Sequence in Nature

fibonacci in nature
Fibonacci as starting point of life. Image:

fibronacci in nature
Romanesque brocolli is a striking example of the fibonacci.

fibonacci in nature
Spiral aloe. Numerous cactus display the fibonacci spiral.

fibonacci in nature

fibonacci in nature
Marlborough Rock Daisy by Sid Mosdell.

fibonacci in nature
All pinecones display a fibonacci sequence.

fibonacci in nature
American giant millipede. The fibonacci is thought to be the design of least resistence. Image by Alan Cressler.

fibonacci in nature
A monarch caterpillar about to form a chrysalis.

fibonacci in nature
Fibonacci and armor = very safe.

fibonacci in nature
Fibonacci in spores. A fiddlehead or koru. Photo by Sid Mosdell.

fibonacci in nature
Snails and fingerprints. Images:

fibonacci in nature
Fibonacci in the wave. Buy the ptin

fibonacci in nature
Water falls into the shapes of a fibonacci during numerous events. Another example would be a vortex.

fibronacci in nature
One blogger has applied the fibonacci sequence to population density and land mass. In Africa the majority of highly populated cities fall on or close to where the spiral predicts.

fibonacci in nature
Shell Fossil via:

Who was Fibonacci?

The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci. Though Fibonacci first introduced the sequence to the western world in 1202, it had been noted by Indian mathematicians as early as the sixth century.

The fibonacci defines how the density of branches increases up a tree trunk, the arrangement of leaves on a stem, and how a pine cone’s scales are arranged. Yet you will not see the fibonacci everywhere, as nature has many different methods and shades of survival.

Hang Fibonacci In Your Home

These prints from can be printed at any size you like—they’ll frame them for you or you can print directly to canvas. We’ve had really good luck with their prints; shipping is fast and the prints are good quality. These start at around $25 each.

THE GREAT WAVE OF KANAGAWA, The Great Wave by Katsushika Hokusai


Fibonacci Spiral by Seymour

babar760-nautilus-shell Nautilus Shell by Babar760

Some stock traders are using the Fibonacci sequence as an attempt to “crack” the stock market, by selling or buying when certain sequences appear on stock charts. Not recommended!

There’s also a Fibonacci betting system. The idea here is to start with an even money bet, like red/black in roulette. You keep moving up the Fibonacci sequence every time you lose a bet on the idea that, eventually, you’ll win and recoup your money. Also not recommended!

The Best Books about Fibonacci and the Fibonacci Sequence

The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number by Mario Livio

Growing Patterns: Fibonacci Numbers in Nature by Sarah and Richard Campbell

The Golden Section: Nature’s Greatest Secret by Scott Olsen

The Fabulous Fibonacci Numbers by Alfred Posamentier and Ingmar Lehmann

Blockhead: The Life of Fibonacci by Joseph D’Agnese and John O’Brien (children’s book, named a Mathical Honor Book April 2015)

Fascinating! A must watch!
Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series.

Check out this Custom Fibonacci Spiral Generator –

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Author: Keiren

Keiren is an artist who lives in New York City. A lover of animals, nature, science & green building.


    (note reference to eleventh proposition of the second book of Euclid)

    Jay Hambidge in the 1920s described ‘Dynamic Symmetry’ and the ‘Whirling Square’ being found in the Greek vase, the Parthenon, and in nature (like the shell and the sunflower head). The Dover reprint cover has an unfortunate, misleading illustration of static symmetry.

  2. another example of the glory and wonder of our God! That is simply amazing… I don’t know what else to say!

  3. Pingback: VII. Hunua Falls – AOTEAROA

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