Friday Fractal XI

i-0b9b803ca8a7c8a0d58f69c6b39444c2-bffwhole.jpgI never did match any of Lillybridge's photography work on my visit to the South Platte. The past seemed to be lost under layers of roadways and rails. Still, within that changed land, patterns of natural beauty still exist. Sometimes, looking through fractals is the same way... there are many complex layers, and sometimes I have to search long and hard to find the pattern I seek. Today's fractal was no different. The lower layers are familiar Julia sets (similar to these) while the upper is a unique formula written by Andras Szolek. His formula is a complex conglomeration based on other fractals. (The image to the right shows my full modification of his formula. Together, they add up to this:

i-fa5849326f72e02c8f9f0cc015824456-bff2.jpg

Here's a similar pattern, as seen in the midst of Habitat Park:

i-58ad99207feb5843d7f7b37e9a3b45b1-butterfly.jpg

A woodland skipper (Ochlodes sylvanoides) darts around near the South Platte, ignorant of the din of traffic beyond.

Even in this polluted, transformed land, native life hangs on. Like the ducks pictured yesterday, this butterfly species has managed to survive along these banks for centuries. I suspect there will be others like these, long after the freeway is gone. I just wonder if anyone will still be watching.

Notes: (3:20pm--Updated the fractal to use a fancier butterfly.) The previous image can still be seen here. All images were created by the author, fractals made using ChaosPro.

More like this

Note: I originally planned to post this along with the Friday Fractal. Then, like chaos, fractals, and life, it didn't turn out the way I expected. Considering the length and tone of this piece, it will stand better alone. Never fear, the fractal is still on the way. "They paved paradise, and put…
Note from your fractalist: Sorry, folks, this one is a day late. I discovered early yesterday that my old website had been hacked. It has been fixed, now, although I plan to eventually remove everything from there, and repost it here somewhere. Just getting the bad scripts out has kept me plenty…
Today's fractal is so bushy and branching, that you might almost miss the regular curving patterns of a Julia set. (Actually, this is two Julia sets, but who's counting?) That seems fitting, as nature can be the same way. You might not notice a particular spot, even though you pass by every day.…
When I joined the crew here at ScienceBlogs, I was given a pledge name: Fractal. Now, you can see why: I'm in love with fractals. As a close friend of mine put it, a fractal is essentially "a tangent off on a tangent off on a tangent off on a tangent...," which described me rather well. It…