Fractals are everywhere in nature - beautiful natural pictures

What are fractals?

Short definition:

Fractals are non-regular geometric shapes that have the same degree of non-regularity on all scales.

More precisely:

A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity.
Roots of the idea of fractals go back to the 17th century, while mathematically rigorous treatment of fractals can be traced back to functions studied by Karl Weierstrass, Georg Cantor and Felix Hausdorff a century later in studying functions that were continuous but not differentiable; however, the term fractal was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."
A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.There are several examples of fractals, which are defined as portraying exact self-similarity, quasi self-similarity, or statistical self-similarity. While fractals are a mathematical construct, they are found in nature, which has led to their inclusion in artwork.
They are useful in medicine, soil mechanics, seismology, and technical analysis.

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Now, here are some natural examples:




Romanesco broccoli or cauliflower


Aloe Plant





Fern leaves

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Leaf skeleton

source: Tom Gourley


Sun flower


Nautilus

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Snowflake


White Peacock

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Delicate ice crystals


Microscopic fractal Geology

Ultraiterator - Dan Wills


Lightning

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I surely missed some, any ideas?

cool pics...star and flag

Beutiful stuff
Nice thread.
Look at these pics and it gives you a sense of everything is much bigger than we think.

reply to post by elevenaugust


Oooo, they are some of the best pictures to demonstrate the principle of fractals in nature. Very nice! I'll probably use some of these pictures in the future when trying to explain chaos theory to people.

This documentary will help people learn more about fractals in nature:

Nautilus shells also portray phi (1.618033...,golden ratio, Φ).

Here's a documentary on fractals featuring Arthur C. Clarke! (Way cools!)

Star and flag.
Fractals are one of my favourite new things that I've come across in the last year. SO glad you posted this for all to enjoy.
Mind blowing stuff, just mind blowing. Even more so when you see the series mentioned above;
THE SECRET LIFE OF CHAOS from the BBC. WELL worth a look

reply to post by elevenaugust


I LOVE fractals and have been generating them for years with various programs.

I get fruit and veggies delivered to my house each month, last year they gave me one of those Romanesco broccoli and I was thrilled! It was so beautiful I waited for days before I steamed it. I had never seen one before and I must say, it was absolutely delicious!!!!

Here's one of my renderings, it is a Mandelbulb.

[atsimg]http://files.abovetopsecret.com/images/member/fb478bcb0889.jpg[/atsimg]

Yeap very cool pics, roots, veins, trees, lightning all that is all related to a all knowing, all powerful Creator Yahuwah, who has His blueprint in everything. Its amazing!

This has more relevance when you substitute the cube for a torus...

Thank you all for your replies and insights!

Here are some more examples of natural fractals:


Trees

Source: Fractal man's Flickr user


Mountain ranges

source


Lung


Fractal-like structure of a real neuron