Simply beautiful! I love how advances in technology (like the ability to view these fractal patterns) allows us to expand art as well as our understanding of the world around us.

these are great and all, but they're all exactly the same.. this is what water carves pretty much no matter what you do. everything is either glacial, a mountain ridge, a river, or a coastline. i was hoping for at least a few spectacular phytoplankton blooms or something unexpected.

Still, it's pretty cool to see some relatively abstract maths manifest itself on such a practical scale.

Here's another site with similar images:

http://www.miqel.com/fractals_math_patterns/visual-math-natu...

It's hard to recommend parts of that site, it's all awesome.

The rest of Paul Bourke's website is also very cool, so don't miss it!

I was hoping someone else would say this. Some time ago I stopped bookmarking sites in the browser, relying instead on the principle of "if it's important, it's memorable"... then I stumbled upon Paul Bourke's page (while looking for a document/date overview for MacPerpective of all things).

I call it the 3-interest rule. If something comes up that I find really intriguing 3 times in a row from 3 independent and reliable sources (books/wiki/long form article/comments) - then I go into deep investigative mode.

I try to soak up as much as I can - not bothering too much with bookmarks because I'll never come back to it in that fashion (I'm driven by slow-burning interests/big problems in my field I always think about coupled with short bursts of deep random investigation into diverse fields that aren't my forte) and trying to integrate as much as I can within my current mental models before moving on to other subjects and only returning when the 3-interest rule is breached once more (it always has with everything I've investigated).

For example: Automation and the reversal of globalisation has come up a few times from various high signal-low volume sources so I went in deep and have concluded that China is dead and the future doesn't need humans - at all (extinction level event).

I just kinda fell into this mode, and this had some effect on my habits:

http://www.cs.virginia.edu/~robins/YouAndYourResearch.html

I wonder how hard would it be to measure their mathematical properties, like fractal dimension. Perhaps using image processing tools. I heard the simple box counting method is not perfect for complex natural structures. Does anyone know any published algorithms?

There is an attempt here: http://bit.ly/SXwFDt

Why a bitly link?

This is fascinating! I would love to know the process that the author went through to find these, i.e. did they just pan over a large area or did they target certain geographic features. It's interesting that there are entries from such a wide variety of countries.

It's amazing to think that some of those random looking squiggles are the center of someone's world. The eye glazes over at the multitude of hills and river bends - but some must be totally unique and meaningful to someone.

I think that proof there is a god can be found somewhere between 'Feedback' and 'Fractals'... would love to check out more information on the mathematics that exist here.

Would it be silly to attempt to analyze an image of a natural fractal in order to approximate the equation which forms the fractals?

Has something like that been done before?

Mandelbrot pushed his discoveries as methods for modeling real-world objects, including things like what you describe. so, the impetus for his popularization of fractals was this practical reason. at least, that's how Mandelbrot promoted fractals

you might be interested in "the fractal geometry of nature" by benoit mandelbrot.

Fantastic! Fractals are beautiful by themselves but when found in nature, they're just that much more amazing

I would like one of these printed and on my wall.

I have bought a couple satellite images from the USGS. The prints are large and very beautiful (and cheap). I would suggest checking it out (sorry for the horrible looking link):

http://store.usgs.gov/b2c_usgs/b2c/display/(xcm=r3standardpi...

Made a backup here: http://imgur.com/a/gFKhN

life imitating mathematics imitating life

These are not fractals. Fractal-like at best.

From http://en.wikipedia.org/wiki/Fractal

"The mathematical concept is difficult to formally define even for mathematicians, but key features can be understood with little mathematical background."

I'm not even sure if saying that something is fractal-like doesn't make it fractal? One of fractal properties is self-similarity. Thus if you say that it is similar to fractals doesn't it make it fractal?

They are at least as fractal as a road can be a straight line.