• 17 Captivating Fractals Found in Nature

    Fractals: they’re famously found in nature and artists have created some incredible renderings as well. Fractals are purely a wonder – too irregular for Euclidean geometry; iterative and recursive and seemingly infinite. They turn up in food and germs, plants and animals, mountains and water and sky. Here are seventeen stunning examples:

    1. Sea shells

    Images via Sustainable San Mateo and Designer

    The nautilus is one of the most famous examples of a fractal in nature. The perfect pattern is called a Fibonacci spiral.

    2. Snow flake

    Images via Popular Science and Daily Dose of Imagery

    3. Lightning

    Images via howstuffworks, moonraker and Yale

    Lightning’s terrifying power is both awesome and beautiful. The fractals created by lightning are fascinatingly arbitrary and irregular.

    4. Romanescu

    Image via docman

    A special type of broccoli, this cruciferous and tasty cousin of the cabbage is a particularly symmetrical fractal. Cook it for your favorite mathematician.

    5. Fern

    Images via red dirt road and travelblog

    The fern is one of many flora that are fractal; it’s an especially good example.

    6. Queen Anne’s Lace

    Image via Chrisjfry

    The delicate Queen Anne’s Lace, which is really just wild carrot, is a beautiful example of a floral fractal. Each blossom produces smaller iterative blooms. This particular image was shot from underneath to demonstrate the fractal nature of the plant.

    7. Broccoli

    Image via American Feast

    Though not as famously geometric as its relative the Romanescu, broccoli is also a fractal.

    8. Peacock

    Images via National Geographic and Neatorama

    Males of both the white peacock and standard peacock variety are resplendent examples of fractals in the animal kingdom. Trivia: the white peacock is not an albino.

    9. Pineapple

    Image via Free Wallpaper

    The pineapple is an unusual fruit that is, in fact, a fractal. Though often associated with Hawaii the fruit is a native of southern Brazil.

    10. Clouds

    Image via daily dose of imagery and Allan Ferguson

    Look outside your window – you may see a fractal cloud at any moment.

    11. Crystals

    Images via gdargaud, Indigo Society, ESRF and Designer

    Both chemically-formed crystals and ice and frost crystals are breathtaking examples of fractals in nature.

    12. Mountain ranges

    Images via USGS, Clemson and Gemland

    Both shorelines and mountain ranges are considered loosely fractal. These particular examples are beautiful.

    13. Trees and Leaves

    Images via timalbertson, Yale, enchanter, background wallpaper

    From the macro view of a leaf to the span of a tree’s branches, fractals turn up frequently.

    14. Shorelines

    Image via Today is a good day

    This stunningly complex fractal shoreline is none other than the pan handle of Florida.

    15. Rivers and fjords

    Images via Today is a good day and e-picworld

    From the midwest of the United States to the icy fjords of Norway, fractals are often viewed by airline passengers – these particular travelers were savvy enough to snap photographs.

    16. Sea urchins and sea stars

    Images via jurvetson and curious animals

    Sea urchins are compact, almost artistic little creatures; sea stars are more commonly referred to as starfish.

    17. Stalagmites and stalactites

    Images via wikimedia, Yale and Good Earth Graphics

    By now you know that stalagmites shoot up from the ground while stalactites form overhead.

    Amazing fractal configurations all. The links at the beginning of this post are highly recommended as they are a great start to exploring even more wondrous natural and artificial fractals.

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    31 Comments

    • User Gravatar Sun
      September 7th, 2008 at 8:01 pm

      Wow! That was beautiful!
      thank you…

    • User Gravatar kabir
      September 7th, 2008 at 10:59 pm

      god, the designer. we are mere specks of his mind, just re-arranging his models.

    • User Gravatar sandra evans
      September 8th, 2008 at 2:23 am

      By now you know that stalagmites shoot up from the ground while stalactites form overhead.

      just wanted to add how I remember which is which,

      the g in stalagmites and the c in stalactites stand for g for ground and c for ceiling
      there is also a latin ref in the words somewhere but Iv’e forgotten that one

      lovely photos :>))

    • User Gravatar web design
      September 8th, 2008 at 8:40 am

      The unimaginable complexity of nature.

    • User Gravatar Jomark Osabel
      September 8th, 2008 at 8:44 am

      highly informative. I guess people are fractals too.

    • User Gravatar Anders Sandberg
      September 8th, 2008 at 12:53 pm

      Great pictures! However, several of these examples are not fractals. The usual mathematical definition (a noninteger Hausdorff dimension) is not true for the seashells, pineapples, peacocks, sea urchins and crystals. Self-similarity is not true for crystals, pineapples and peacocks. In particular crystals are very non-fractal since they look extremely different globally (a polyhedron) and locally (a plane). That said, many crystal masses do seem to have a fractal structure with facets on all scales.

      In the end, these pictures are beautiful examples of complex systems. But it is hard to find any neat definition that sums up them all – most are created through recursive application of rules, but that is not enough to guarantee complexity, fractality or beauty on its own.

    • User Gravatar CB
      September 9th, 2008 at 4:38 pm

      I learned about stalagmites and stalagtites in school around the same time that I started wearing tights (”hose”). I remember which was which of stalagmites and stalagtites by “tights comes down”. I’ve been able to distimguish between the two ever since.

    • User Gravatar norm
      September 10th, 2008 at 3:44 pm

      It’s not god or design, it’s math and physics, but we’re still specks.

    • User Gravatar felapp
      September 10th, 2008 at 6:04 pm

      OMG how beautiful….Too bad “intelligent design” has been turned into a PI term.

    • User Gravatar Elisha
      September 13th, 2008 at 8:44 am

      Wow! That is insane – so beautiful. I have heard about fractals, but I didn’t realise they could be found with such diversity in nature. Thank you!

    • User Gravatar ccrow
      September 28th, 2008 at 6:44 am

      Beautiful pics! I have always thought the chambered nautilus shell is one of the most perfect structures is nature.
      Thoughtful comment, mr/ms vubzcgois, if that is, in fact, your real name.

    • User Gravatar captivating capiz blog
      October 4th, 2008 at 7:42 am

      I like the picture of the nautilus perfect, I’ve seen it once in our school library way back in my high school days and I was really captivatingly captivated by the perfect symmetry that the shell had developed over the years of the growth of the resident inside it.

    • User Gravatar Jeanne Khan
      November 2nd, 2008 at 6:42 pm

      PBS bit re: fractals left me touched to the core.
      The patterns repeating to the nth degree were
      exquisite. My atheist/humanist self bowed to
      the humans whose minds moved beyond Euclid
      and Pythagoras to another realm. Stunning stuff!

    • User Gravatar Eddie Coffey
      November 12th, 2008 at 5:24 pm

      i8unu83jd9nnr6o1

    • User Gravatar O.L. Samaranayake
      November 16th, 2008 at 9:17 am

      It was great. I enjoyed it. Informative.
      Tks.

    • User Gravatar web
      December 4th, 2008 at 7:18 am

      Awesome shots, thanks.

    • User Gravatar Jimmy Wade
      January 14th, 2009 at 9:29 pm

      So beautiful! Too bad they’re just the result of random evolution!!!

    • User Gravatar mike
      January 18th, 2009 at 3:17 am

      ZKsmos hi! how you doin?

    • User Gravatar Judy
      January 23rd, 2009 at 1:26 pm

      Beautiful! Fractals or not they are lovely pictures and wonderful examples of Gods handiwork! For all those people who have a problem with God they should read “The Shack” by Wm. Paul Young. The word fractal is mentioned in the book and is why I looked up the word. Anyway, for anyone interested – God knows you and is very fond of You!

    • User Gravatar sam
      March 15th, 2009 at 12:04 pm

      these pictures are making me stick to this,. i am short of words to say awesome stuff

    • User Gravatar Steve Roders
      April 11th, 2009 at 6:06 am

      I’m so siked I see this everywhere. Thought I was crazy. Amazing how fractals are everywhere. They’re also in and shadows and bright light. Amazing awesome website

    • User Gravatar holly
      May 15th, 2009 at 11:03 am

      i have a math project due this upcoming wednsday and i have absolutally no clue how things like ferns and some roses are fractals because its not like they are just a pattern because they are actually like

    • User Gravatar custom joomla development guy
      May 30th, 2009 at 9:19 am

      this is AWSOME! Thanks a tons

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