How much control do you have in making these fractals?

February 20, 2022

I am often asked how much control I have over my fractal images. If the images are based on algorithms, can you really make it do what you want?

Let’s look at a new design I have been working on.

This one looks promising, with its periodic recurrence function and a single orbit trap. But the giant blue rings are covering up the interesting fine detail in the background and are a bit overwhelming. So I can instruct the algorithm to skip drawing anything during the first iteration, which will remove the blue rings.

Now we’re getting better. This is where I start making tweaks to the orbit trap dimensions or recurrence function coefficients. Here is one minor variation made by increasing the vertical offset of the orbit trap. Is it better, or worse? It’s a bit like an eye exam, and since there are literally infinite possibilities, I can sometimes spend hours making little adjustments trying to get the shapes just right or discover new interesting features.

What I cannot do (without cheating through Photoshop, which I refuse to do) is make little "touch-ups" to one spot or another. I can’t do anything like remove a single blue ring in the corner, for example.

Of course, the image is one view into the full plane of this fractal’s existence. There are also infinite other places to look within the fractal. Think about looking at a map of the United States, versus a map of New Mexico or California. They’re all the same world, but different parts. The maps can also have different shapes - such as square, landscape, portrait, panoramic - so when selecting different views, I also need to consider shapes that are common and easy to print, like an 8” x 10”. Here are a couple different views of the same fractal.

Finally, I can adjust colors. This is one thing I have complete control over, at least within the constraints of what colors that can be reproduced on a computer screen or printer. Here’s an orange variation of the same fractal.

As a fractal artist I may not have as much freedom as a painter, for example, but there are still plenty of knobs to turn and infinite possibilities for art. Which variations are your favorites?