17 Captivating Examples of Fractals in Nature

17 Captivating Fractals Found in Nature

By Ecoist in Animals & Habitats, Featured Articles, Nature & Ecosystems

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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

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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

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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

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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

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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

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Image via daily dose of imagery and Allan Ferguson

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

11. Crystals

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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

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Images via USGS, Clemson and Gemland

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

13. Trees and Leaves

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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

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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

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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

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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.

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 :>))

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.

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.

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.

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!

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!

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