Fridayish Lichenish Fractal

I suppose, if I wanted to make things easier, I would just start calling these the "Weekend Fractal" but it just doesn’t have the same ring. Besides, this week, Carl Zimmer beat me to the Friday Fractal, on naked skin even. (The owner of the fleshy fractal shares some interesting insights on his Julia set; be sure to check it out.) Still, I had this section of a Mandelbrot set lying around, whose autumn hues would be ill fit if posted later in the season:


You can see where this slice fits in to the entire set in this short movie:


Here, if anyone would like it, is a large copy of the whole set in .jpg form, as the animation takes a while to load, and isn’t that clear.

You might notice the fuzzy filling in the middle isn’t typical for the Mandelbrot set. I used my favorite fractal effect, a simulation of fractal Brownian motion, to color the inside. I was hoping it might imitate the weathering granite lying beneath this patch of lichen and moss:


Lichen and Moss on Granite

Lichen seems like the perfect subject for fractal imitation. The organism has a sort of beautiful complexity all its own--it is a symbiotic relationship between a fungus and an algae. It also manages to play an small, yet important role by gradually weathering the rock it grows upon, releasing minerals which will be washed away into a nearby stream. Those minerals are drawn into the flora growing along the shore, feeding the poplars, pines, and grasses, which provide food and shelter to a variety of animals. This crusty-looking, greenish-yellow fuzz can move mountains and help feed an entire ecosystem. Talk about sensitive dependence on initial conditions....

Before I go, here is one more lichen picture:


It almost seemed as if the prickly pear growing next to the rocks was in competition with the lichen. Other prickly pears, growing near bare boulders, tended to be more shriveled, as if the heat reflecting from the stone cooked out all available moisture. Growing near the lichen-covered rocks, however, this prickly pear flourished. The lichen beneath the cacti, however, did not seem to benefit. Dead, gray patches stand out almost in the exact shape of the prickly pear shadow. It’s a far flung speculation, I’m sure, but I think the lichen and the prickly pear may be at war.

Photos of lichen were taken by the author near Table Mesa, in Boulder, CO. Fractals made by the author using ChaosPro.

More like this

Life is complex. The last week has been particularly so for me, but I’d rather not go into details about it. So, I’m keeping this week’s fractal somewhat on the simple side. I suppose in fractals, just like life, simplicity and complexity are often found side by side. I’ve always liked to describe…
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…
Maybe it’s because it’s nearly summer. Maybe it’s because I finally finished my finals. Maybe it’s all a result of coincidence and random web browsing. Whatever the reason, I feel like filling my blog with warm, happy colors this weekend. What better place to begin, than with a fractal? A Fractal…
Even in a snowy winter landscape, I feel as if I'm surrounded by fractals. In order to capture this feeling, I turned to the complex topography of the Mandelbrot set. I added an fBm coloring algorithm, to mimic the soft hues of a winter storm. When the fractal was complete, I decided to superimpose…