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Saturday, September 23, 2023

"Oh Fractal Tree, Oh Fractal Tree"

“Oh Fractal Tree, Oh Fractal Tree

Thy leaves are so repeating…”

Okaaay... that was bad. It’s September, the mid-point between the nostalgic and/or “plan WAY ahead” vibes of “Christmas in July” and the ramp-up to the coming holiday. It’s hard to express the spirit in the right way when there are so many distracting Halloween displays for candy and decorations.

But here we are, and I’ve been busy with fractals again. I discovered one called a Sierpinski tetrahedron which is like a Sierpinski triangle that escaped Flatland to become a pyramid.

Here’s a video animation displaying how a basic one is constructed.

After getting one set up in my fractal program, I started playing with it, distorting the transforms and shifting them about. When I realized it had taken on the shape of a beautiful, wild evergreen, I changed the color gradient to suit it, including a bit of white that could pass for snow.

But this wasn’t enough. I wanted it to be in a setting that would highlight the wild character I saw in it. And I wanted to do that in a single fractal, without editing different images together.

I'd learned about manipulating something in the fractal program called XAOS (pronounced "chaos"). Each element of the fractal interacts with the others and each part changes the others. The whole thing, after all, is one big mathematical computation, and if you alter the numbers within it or insert additional factors, it changes the final result. Manipulating the XAOS controls how much each part impacts the others. (That's about as simply as I can put it give that I expect this to be read by people who are not using fractal programs.)

At first, I’d hoped to add something of a landscape beneath the tree, but my experience with this art form is still quite limited and those efforts were not fruitful. Then I thought a star would complement the scene and had better luck there. I’ll admit, I’d had hoped to position it directly over the top of the tree to imply a tree topper provided by nature but could not get it to comply. Perhaps that was fortunate as I think it looks better where it ended up. Rather than white, I set the color to a pale, icy pink within the chosen gradient. If you look closely at the swirls of light emanating from the star’s center, you’ll notice the shape that is the tree, and which makes up the tree. Fractals are amazing.

This “Sierpinski Tetrahedron Evergreen” image is available at Zazzle on a collection of various holiday stationery and a few other items. If you'd like to have it available on another item, please contact me.


Thank you for visiting, and I wish you a magnificent autumn!

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