Chaotic Utopia

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:

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

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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.