On Fibonacci in Nature

Nature has many patterns, and they come in a variety of ways. Patterns can be simple, inspiring, microscopic, overt, sudden, gradual, and who knows how many ways as seasons, tides, anatomical structures, life created, processes, and behaviors. Patterns are associated with animals, plants, and the microscopic world.

For instance, the chambered nautilus is a biological relative to snails, squids, and octopi. Even though it is a simple organism, we stare with wonder at its shell and subsequent design. This mollusk also inspired Oliver Wendell Holmes to write the words below (taken from this poem named for its inspiration).

Build thee more stately mansions, O my soul,
As the swift seasons roll!
Leave thy low-vaulted past!
Let each new temple, nobler than the last,
Shut thee from heaven with a dome more vast,
Till thou at length art free,
Leaving thine outgrown shell by life’s unresting sea!

The Fibonacci sequence is a mathematical pattern linked to many patterns in nature. Tied to Leonardo of Pisa work in the early 1200s, the sequence appears in eastern cultures even earlier. The sequence can appear as a mathematical equation, a graphic representation, or in a photograph that may be just an image to the untrained eye.

Nonetheless, patterns in nature speak in their own language to help us understand the glories of the creation in which we live. Maybe this is one of the messages Dr. Seuss’s professes in these words:

I am the Lorax. I speak for the trees. I speak for the trees for they have no tongues.” —Dr. Seuss (The Lorax)

Enjoy this wonder video about the Fibonacci sequence in nature … and a special thanks to Kellie at The Beaglez for sharing this video with me. Below the video, I posted several photography links for anyone wanting to see more wonderful images.


38 thoughts on “On Fibonacci in Nature

  1. I gotta stop visiting car sites before reading your posts. I didn’t see a nautilus shell, I saw a turbocharger casing! (Which, interestingly enough, are very similar in shape – pull the air in or blow the exhaust in via the curve to spin turbine blades. Art as science. 🙂 )
    And I don’t know what the “137.5” degree angle was about (having no sound), but here’s a tidbit from military history. A widespread gun size, used as main armament on small ships and as secondary armament on battleships, was 138.6mm, or 5.46 inches. An odd size, evolved from an early black powder weapon. Suspiciously close to the magic 137.5 degree angle oft-shown, eh?
    (Hey, it’s weak, but it’s all I got right now.)
    Or you can go for the heavily parodied but still dramatic “double infinity” theorem. An atom is really a solar system with a star for the nucleus and planets for the elections, and our solar system is simply an atom in the fingernail of some giant life form. Run that past a friend when he’s drunk or wasted, and watch his brains ooze out his ears! 😀
    Great show, Frank, thanks!


  2. Impressive! I have always loved the chambered nautilus for its simple granduer–and now I have a better understanding of why I sound it so enthralling. Thanks for sharing. A few months ago I posted a video that shares a musical interpretation of the new controversial circle constant called tau–it presents an appealing pattern as well. But I like the visuals of yours better!



    • Patti,
      Kellie posted this video not that long ago, so it had time to simmer in my head .. .then I finally got time to write … and as sometimes happens, it all comes together. Glad you enjoyed it … and thanks for sharing your link. That is such an awesome video … OH NO … another one for me to dive into the depths to ponder. Many thanks!


  3. I posted Nature By Numbers a while back. As far as I’m concerned, it’s one of the most beautiful videos ever. I’ve got to come back when I have more time, just to check out those links!


  4. I love the piano, it makes it so much more epic.I wonder if it’s being played backwards, he he.

    I love The Lorax. I think it might be the first book with environmental themes I ever read. I think I’ll blog about that some day soon.

    I wonder what else follows the Fibonacci sequence. Do blogs?


  5. HI Frank,

    Thanks for the shout-out – and for showing the beauty inherent in our small creatures and big world! And thanks for more links to amazing visuals. Always good to clear the head from the tyranny of the immediate.


  6. Hi Frank:

    Thanks for placing the link to my “Patterns In Nature: Images From A Camera” photo gallery. A nice surprise upon Googling your blog site. I now have a blog on Patterns In Nature as well.



    • Bill,
      Welcome first-time commenter, as well as a pleasant surprise from a past post … and actually a post that I really enjoyed creating. Thanks for the heads up on your new site as I will visit. Many thanks for taking the time to let me know.


  7. Pingback: Fibonacci, What a Notion! | composerinthegarden

    • Cuttlefish,
      I checked it out. Seems that the video is now blocked, so I replaced it … and it may be the same one (but I’m not sure). Thanks for discovering the problem for me (yet sorry you had the problem).


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  9. Fibonacci numbers are also widely used in financial charting software, for example to provide estimates of retracement levels after a market swoon. Some financial forecasters like Robert Prechter think Fibonacci numbers underlie basic human responses to market events.


  10. A beautiful piece on the fibonacci series. Were I a school superintendent I would ask all the math and science teachers to show this to their classes at the start of each. Message: engineering and science are creative disciplines with endless possibilities.


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  12. Yes, the golden ratio is very much connected to the Fibonacci numbers. For example, the Binet’s formula for finding the nth term of a Fibonacci series is highly based on the golden ratio


  13. Pingback: On Exploring a Musical Design – A Frank Angle

  14. Reblogged this on FIAT LUX and commented:
    Nature has many patterns, and they come in a varuety of ways.
    Patterns can be simple, inspired,microscopic, overt,sudden, gradual,
    and who knows how many ways as seasons, tides, anatomical structures, life created, processes and behaviors.
    Patterns are associated with plants, animals, and the microscopic world… but also with human fractals and galaxies…


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