Notice: The links of products and designs for sale on this site contain cookies in the form of a referral code. The purpose of this is simply to allow me to receive credit for any purchase you may make as a result of having visited my blog first. This does NOT provide me with any information about you or impact the price you pay for any merchandise, but it will increase my commission. If you object to this, simply do not click on any such links. (Links to contest entries and art not stated to be for sale do not contain cookies.) Thank you for your support and understanding.

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!

Tuesday, January 24, 2023

For the Love of Fractals

 As I mentioned in my last post, I’ve been exploring fractals, patterns composed of repeating and evolving iterations of themselves. Here are some simple examples that may be familiar to you. 

Sierpinski Triangle

Koch Snowflake  A fractal tree

I’d heard them mentioned in various contexts suggesting such things as the potential for them to provide a form for understanding patterns in time. I wanted to understand them better, and as an artist, the most logical way was to learn to create them visually.

There are numerous shareware programs for this available, and I chose to start with Apophysis. Basic tutorials on the program were hard to come by and never comprehensive enough for my curiosity, but I found enough to cobble together a basic understanding and get on with creating my own images. It’s a completely unique creative experience as all are made purely via mathematical formulas programed into the application, and each of these has a number of variables to tweak resulting in infinite possible settings. The artist must become familiar with the type of image produced by particular variations.

That almost sounds simple enough until you consider that different variations do not merely overlay one another when combined (though there are techniques to make that happen). Instead, they merge into a different form. It’s easy for the combinations to result in a blah mess, but hone the numerous variables just right, and a beautiful design crystalizes before your eyes. It makes me think of The Beatles, one of the most popular music groups in modern history. Together, John, Paul, George and Ringo—the right guys and the right time—merged into a synastry that struck a chord with the masses. While each of them went on to further success in their solo careers, none reached the same level as they had together. The sum was not only more than the parts, but a unique entity.

Since the love that connects two people also reflects the idea of patterns resonating to create something unique, something that lights up when combination is just right, it feels appropriate that the first fractal design I share is one I’m publishing on a Valentine. 

"Fractal Love"

Rings filled with hearts, overlapping and extending into eternity, rolling through a rainbow of repetition just as a couple’s many shared moods and experiences are grounded in the form they create by their union.

“Fractal Love” is available on cards and other products at Zazzle. If there’s another product you’d like to have it on, you’re welcome to contact me and request it.


"Fractal Love" iPhone Case     "Fractal Love" Lumbar Pillow     "Fractal Love" Leggings

Wishing everyone Peace, LOVE, and Joy on every day of the year. Thanks for visiting and please come again!