Friday Fractal XLIV

i-86086751487eb4efef466f8f0c922415-bdcfwhole.jpg

Tracking wildlife in my neighborhood wetlands this week made me reflect on the complex network of organisms in a habitat. Everything in an ecosystem is so intimately tied together, that a single species can have drastic effects on the entire habitat. The ecosystem, like all systems containing that elusive chaotic aspect, has sensitive dependence on the initial conditions... like a fractal. In the fractal or in nature, one small change can ripple through the entire set. For an example, I took two copies of the classic Mandelbrot set, and laid one atop the other. Then, I used slightly different coloring algorithms on each set; Perlin noise on one and an Epsilon Cross variation on the other. Then, I applied a lake transformation to each set, which mirrors the image and ripples the lower half, to simulate a reflection on water. Pooled together, here's your dam fractal:
(no, I will never tire of that pun)

i-8300e697b17ea9e4c10f95b743557bdc-bdcf.jpg

And the beaver dam which inspired it:

i-beb84b660b5dc65481ef8efe3a3aa3b7-damBDC.jpg

A beaver dam on Big Dry Creek, at BioBlitz Site B.

Here, as in the fractal, complex patterns lie atop one another, interacting in such a way as to create an exotic environment. Big Dry Creek, meandering across Rocky Flats and across the city of Westminster, is lined by centuries-old cottonwood trees. The creek has dug deep furrows into the earth, leaving steep banks along each oxbow. All is still. Until... a family of beavers moves in and changes the entire landscape is quickly transformed.

i-4d1cb7427e256bc4c6473dce5754cd11-gnaweduptree.jpg

They bring the giant cottonwoods crashing down, and divert the water's flow. Steep banks erode, giving way to the widening ponds. Every spare bit of debris--twigs, plant material, or discarded bits of fast food containers--is placed into the dam. There it begins to decay, turning into the muddy glue which holds the dam together. Eventually, the dam changes the entire course of the stream. The once dry shores, where the remaining trees take root, are flooded over, leaving naked limbs rising from the water. Those strong, yet barren, branches attract other wildlife, herons, ducks and geese, while the slowed, stagnant waters beneath host amphibians and fish.

One species shows up, and transforms the entire habitat. If you ever doubt that small changes can make a big difference, take a stroll along Big Dry Creek.

But...if you can't make it to Westminster, Colorado... go reflect on a dam fractal.

All images by the author, fractals made using ChaosPro.

More like this

If we look at the natural world around us, fractals abound. Sometimes, not. This is the greatest puzzle to me... not that fractals appear in nature, but the fact that not everything is a fractal. Working on this week’s layered set (which took a while, mostly due to unrelated circumstances) I found…
In theory, conducting a bioblitz was going to be a simple enterprise. I would go to one of my chosen spots, count the organisms as I went along, noting them in my book and, if possible take a photograph. I figured the two places I'd chosen would be relatively barren. In the tall grass prairie (…
Today is Earth Day, the perfect holiday to kick off a little Blogger Bioblitzing for National Wildlife Week. All around our bumpy sphere, people are going out and getting intimate with nature. Like many other bloggers, I've been scouting out the perfect places to bioblitz. In Colorado (as…
Hidden deep within the layers of the Mandelbrot set, subtle, yet familiar forms can almost leap out at you. This happened to me as I applied the coloring formula (based on Gaussian integers) to this week's fractal. I was merely looking for a pattern that was somewhat spotty. I ended up with this…

And sometimes there are tasty Brook Trout!

I've had the pleasure of being around beaver ponds and fractals. Both are endlessly fascinating and you have combined the two in a unique way. Thanks.

By Crudely Wrott (not verified) on 28 Apr 2007 #permalink

I've started a climate change project called proxEarth.org. Many people have blogs, websites, and use social software sites (social networking, social bookmarking, photo and video sharing, etc.). Some standards for tags and text on blogs, websites, and social software sites could turn the whole global Internet into a kind of Web 2.0 participation platform for climate change. Iâm suggesting a few simple standards for tags and text that leverage processes of the sustainable ProxThink growth model. To get this going, we need people to adopt and use these standards. The project could also use contributors, collaborators, partners, funders and sponsors. To find out more, see: