Since it is the beginning of June, my fractals will probably be increasingly summer-like. You know, flowers, bugs, clouds, trees–those pleasantries which add up to beauty of a summer day. Today, as you can see, is no exception. (I had to drag myself back inside to do the fractal–I could be out there taking nature photographs all day and never get bored. Unfortunately, my son and my dog both do.)

First, a bit of the technical stuff: In today’s fractal, I was trying to imitate two similar forms which are often found together. It seems appropriate, then, that the formula I used to create the Julia set allowed different functions for the two variables in a section of the fractal. (The z*z, each z being a point in the complex plane.) That said, here it is:

And, similarity in nature:

A two-striped grasshopper (Mealanoplus bivittatus) rests on a spike of prairie cordgrass (Spartina pectinata.)

Before the urban sprawl came, my neighborhood was on the outskirts of a vast tall grass prairie ecosystem. Remnants of it are still here, like this clump of grass growing near a ditch. There were hundreds of grasshoppers nearby, including this little guy, who was about a centimeter long.

These grasses grow in clumps up to six feet high–over my head. Unfortunately, along with the black-footed ferrets and other inhabitants of the tall grass prairie ecosystem, they just aren’t where they used to be.

Some people call these weeds and pests… I like to think of them as the original landowners.

When in bloom, the prairie cordgrass bears tiny yellow flowers, as you can see below. When the entire field is blooming, it looks sort of like a flowing, yellow sea. I think that might be what inspired Katherine Lee Bates to write “America, the Beautiful.” In fact, she even used the word “sea” in this quote, as she described of her first impression of the Colorado grassland from the top of Pike’s Peak:

“One day some of the other teachers and I decided to go on a trip to 14,000-foot Pikes Peak. We hired a prairie wagon. Near the top we had to leave the wagon and go the rest of the way on mules. I was very tired. But when I saw the view, I felt great joy. All the wonder of America seemed displayed there, with the sea-like expanse.” (quote found here)

Note: All photographs taken by the author. Fractals were created by the author, using ChaosPro.