Heated Arguments and Melting Fractals (Fractal LXX)

Something about climate change makes people want to argue. Take Greenland, for instance. A few weeks ago, I posted a photo essay about the recent acceleration of melting in the Greenland Ice Sheet. Not only is the entry is still getting comments, but it also spurred a discussion on a political message forum that went on for six pages. Watching all these opinions fly, there were a number of times that I wanted to dive in and start defending science... but I’m a hermit, and it is more fun to lurk and watch. Besides, every point that I wanted to bring up can be found in a paper I’ve been waiting to post here. (Waiting for what? I don’t know... tomorrow, perhaps.)

While everyone else has been arguing about climate change, I recently found myself discussing a most unusual topic: Can fractal art raise awareness concerning climate change? You can guess my answer; yes, when it is paired with good information. If you’re a regular visitor to my "Friday" Fractals, that probably seems like a no-brainer, but I was talking to people who think of fractals as psychedelic swirly pictures with garish 1970s colors. So in order to change their minds, I had to explain what fractals were in order to show how they were relevant. But, before I share an edited version of my defense, here’s an appropriate fractal:


Greenland Melting (A variation on the Mandelbrot set)

and a similar sight in nature:


The Main Greenland Tongue

Now, on to fractals and environmental science (with a couple more images from Greenland to compare to the fractal above.)

Even setting their pure visual appeal aside, I think fractals are an appropriate choice. A number of aspects of fractal art correspond to environmental science in both literal and intuitive ways:

  • Complexity: A fractal is (mathematically) based on complex numbers, and so is drawn on the usual x/y plane with an extra dimension of depth. (A complex number is described by two parts, an imaginary number and a real number.) When we study a complex problem like climate change, we use the usual experimental science, but with an added interdisciplinary "dimension." Many different branches of science (geology, climate science, ecology, chemistry, etc) merge on the same plane to examine an overall pattern, i.e. global warming.
  • Sensitive dependence on initial conditions: this is a fundamental aspect of both the fractal and the patterns in nature which science examines. In a fractal, a slight change to one variable in the initial settings will produce a drastically different image. In our climate, a relatively small addition of carbon dioxide into the atmosphere can result in drastic changes in temperature.

i-c1d163d4289ebe1bca65638c2636e71a-speedingmelt.jpgOverall, a fractal shows that something based on complex variables can be both fascinating and understood... When mathematicians in the late 19th century tried to use fractal equations, they were hopelessly lost without the use of a computer. (The man who first described the Julia set never actually saw it drawn.) With the invention of computers, fractals could finally be drawn, and they were discovered to be intuitively beautiful patterns--which anyone could enjoy--in addition to being mathematically interesting. In the same respect, computer technology and advancements in science have come to provide tools which allow us to look at complex processes in our climate.

I hope that when someone looks at a fractal image in a science-based context, their initial reaction will be "oh, that looks cool." If they are tech-savvy enough, they’ll grasp that it is a graphed image, mapped by a computer. [Some of the initial complaints I heard were that some of my fractal images looked too "real".] When they next look at the images associated with the pattern, the real things in their world that they’d like to understand, maybe they’ll have an extra dimension of curiosity.... maybe they’ll be on the lookout for some complex new edge. They might even realize that with the right tools, they can easily tackle other scientific concepts.

Of course, when discussing science, many prefer to turn to peer-reviewed sources, so my analogous descriptions will probably fall a little short. There are a plethora of studies which have revealed fractal patterns in nature; first and foremost of these would be Benoît Mandelbrot’s paper, published in the March 1983 American Journal of Physics (Volume 51, Issue 3, pp. 286-287), titled "The Fractal Geometry of Nature", (doi:10.1119/1.13295). Many more examples can be easily found. "Science" has published well over 400 scientific papers using fractals in different branches of science, from cosmology to biology and back.

Certainly, I wouldn’t expect anyone to try to fully grasp the usefulness of fractals in science, any more than I would ask them to understand the formulas which generated the fractal they’re looking at. I don’t feel it is necessary to understand the purpose of the fractal in order to enjoy it... or to be inspired by the fractal’s tribute to complexity. On the other hand, if they are curious, the information is out there. [Perhaps fractals really are an essential aspect of nature, but often missed, like the hidden bulk of the iceberg beneath the surface of the water.]


A small fishing boat is dwarfed by icebergs in the Jakobshavn ice fjord, West Greenland

Image of tongue via NASA, small speeding melt image via the BBC, iceberg image via Nature, fractal made by the author using ChaosPro.


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I see fractals as describing patterns in nature in the same way that the Fibonnaci sequence does - only for more complex patterns.

That's not a bad insight, Karl. The Fibonnaci numbers themselves follow a sort of fractal iteration... they are a type of Lindenmayer System, along with Koch Snowflakes, Cantor Dust, and the type of rules that create colonies of algae, tree branches, and ferns.

Human perception translates sensory input in a colorful and 4 dimensional image with additional attributes of solidity, sound, smell, taste. However frequencies of light are mathematical formulas, not color per se. Audio frequencies are mathematical formulas, not sounds per se. Natural laws are mathematical formulas. I suggest we are looking at most natural and complex fractals, which interpreted in the mind produce the image we perceive.

i love the pictures

By Amber keener (not verified) on 08 Dec 2008 #permalink