Friday Fractal XLIV


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)


And the beaver dam which inspired it:


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.


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.

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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

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