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Fractal Imagery and My Digital Art

Updated on January 16, 2018
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Cynthia is a digital marketer, writer, and artist. She writes about a variety of topics, especially digital marketing, languages & culture.

I call this fractal "Ice Age."  I manipulated the colors so that they would all be "cooler."
I call this fractal "Ice Age." I manipulated the colors so that they would all be "cooler." | Source

Fractal Explorer - At Least I Felt Like One

Not too long ago, I came across a hub by Movie Master on dandelions. I was interested in reading because I always have tons of dandelions growing in my yard, along with tons of other weeds – I live near a large National Forest. I’m always game to see what I can do with the plants in my yard - both the ones I can cultivate and ones that grow wild.

But then I saw something in Movie Master’s hub: “kaleidoscope” versions of dandelions. The images were stunning.

For my hubs and in general, I love taking photos. While I wouldn’t call myself a professional photographer, I would say that I’m proficient at image editing. But I was surprised that I hadn’t seen a “kaleidoscope” filter in all my image-editing wanderings.

I promptly opened up GIMP– my image editing software. I looked and looked for the kaleidoscope filter. I went to their website and discovered that the kaleidoscope filter had essentially been replaced by “fractal trace” and “fractal explorer.”

I had no idea what those meant. I vaguely remember fractals from math classes in college, but never did much with the idea of them.

The Move to Digital Art

I really had no idea.

I had no idea that finding fractals would lead me to explore a whole new art medium.

I had studied art in college, taking enough classes to garner a minor. I always wanted art to be a significant hobby of mine. I had been a painter – acrylic on canvas was my favorite medium. The American Southwest inspired my subject matter.

Unfortunately, I lived (and still live) in the southeast. Though I enjoy where I live, selling southwestern art in the southeast proved to be futile. I all but gave up.

Then I saw Movie Master’s hub. I discovered fractals. I have been creating fractals and digital art at a furious pace ever since then.

"Ocean Peaks" is another fractal I created when I first started exploring the world of fractals.
"Ocean Peaks" is another fractal I created when I first started exploring the world of fractals. | Source

What Are Fractals?

At its most basic level, a fractal is a pattern that can repeat over and over again. It can be modeled using a mathematical equation. However, it is an irregular pattern.

Nature herself features fractals all over the place. Hurricanes, tornadoes and other weather events can generate fractal patterns, but even water draining down the sink creates a pattern. The way ferns propel their winding tiny ferns into the air to how other plants grow their leaves create intricate natural patterns. Even the flames in a fire can be interpreted using fractals.

You can take those mathematical expressions and actually render a digital image with them.

Now, I don’t claim to be a mathematical genius. But it is quite thrilling to know that these patterns can be rendered using various mathematical formulas.

In GIMP, I took an image and used “fractal trace” and “fractal explorer” to create a few early images:

One of my earliest fractals.  It's called "Splat."
One of my earliest fractals. It's called "Splat." | Source

Rendering Fractals

Once I made a few images, still didn’t know much. There is an entire world of knowledge to be had in exploring fractal dimensions. I figured out that I could play with the colors by changing things like the sine, cosine and iterations (number of turns or passes) of the image. GIMP would happily do all that for me.

But, I did find my limits with GIMP. Despite the fractal trace and fractal explorer functions, I found that I wanted to be able to manipulate the images even more.

I came across a math book with a beautiful, swirly cover and quickly realized it was a fractal, but a very complicated-looking one. The fractals I had been creating looked quite simple by comparison.

I pressed on. I hopped online to see what more I could do with fractals. I found another program called ChaosPro.

After a brief and free download, I immersed myself into the world of fractals.

Using Fractal Generator Software

Once you open up the program, you have many choices of what types of fractals to make. You can make 3-D images or 2-D images.

Believe it or not, I actually prefer the 2-D images because the 3-D images remind me of body parts…and not in a good way.

One of the easiest ways I get started is by going to the menu bar and choosing “Distribution.Par” – this will generate a 2-D fractal. You can see, though, that there are many choices. Unlimited types of fractals can be generated.

Click thumbnail to view full-size
One of the easiest ways I get started is by going to the menu bar and choosing “Distribution.Par” – this will generate a 2-D fractal.  You can see, though, that there are many choices, indicating that many types of fractals can be generated.Once I have chosen the “Distribution”, I go onto the next sub-category and choose a fractal pattern.  In this case, I chose “Fantasia.”  It’s one of my favorites.After the image comes up, now I can “play” with it.  I can play with the colors using some of the presets.  Playing with the colors.By zooming in, I can home in on an interesting part of the image.  I have double-clicked and zoomed in about 4 times.  You can see that even though I zoomed in, the pattern continually repeats itself.Playing with the colors a little more, zooming in and focusing on a particular area yields this image.You can see the formula that you’re working with over on the right:Now, going over to the area called “mapping” I’m going to effectively change the fractal formula.  I go over to “Ultra Fractal” and then to the subfolder “dmj.ctr” and select “spiral cut” and the image changes.The image after I applied a "spiral cut."Then, in the same folder, I selected “unspiral.”  You’d think that it would straighten the fractal out, but it actually does more to “spiral” it than anything.  Taking out the “unspiral” filter and adding “crazy spiral” adds an unexpected element.Tweaking the image further and adding a “mirror” filter changes the image still: That’s an image that I like!
One of the easiest ways I get started is by going to the menu bar and choosing “Distribution.Par” – this will generate a 2-D fractal.  You can see, though, that there are many choices, indicating that many types of fractals can be generated.
One of the easiest ways I get started is by going to the menu bar and choosing “Distribution.Par” – this will generate a 2-D fractal. You can see, though, that there are many choices, indicating that many types of fractals can be generated. | Source
Once I have chosen the “Distribution”, I go onto the next sub-category and choose a fractal pattern.  In this case, I chose “Fantasia.”  It’s one of my favorites.
Once I have chosen the “Distribution”, I go onto the next sub-category and choose a fractal pattern. In this case, I chose “Fantasia.” It’s one of my favorites. | Source
After the image comes up, now I can “play” with it.  I can play with the colors using some of the presets.
After the image comes up, now I can “play” with it. I can play with the colors using some of the presets. | Source
Playing with the colors.
Playing with the colors. | Source
By zooming in, I can home in on an interesting part of the image.  I have double-clicked and zoomed in about 4 times.  You can see that even though I zoomed in, the pattern continually repeats itself.
By zooming in, I can home in on an interesting part of the image. I have double-clicked and zoomed in about 4 times. You can see that even though I zoomed in, the pattern continually repeats itself. | Source
Playing with the colors a little more, zooming in and focusing on a particular area yields this image.
Playing with the colors a little more, zooming in and focusing on a particular area yields this image. | Source
You can see the formula that you’re working with over on the right:
You can see the formula that you’re working with over on the right: | Source
Now, going over to the area called “mapping” I’m going to effectively change the fractal formula.
Now, going over to the area called “mapping” I’m going to effectively change the fractal formula. | Source
I go over to “Ultra Fractal” and then to the subfolder “dmj.ctr” and select “spiral cut” and the image changes.
I go over to “Ultra Fractal” and then to the subfolder “dmj.ctr” and select “spiral cut” and the image changes. | Source
The image after I applied a "spiral cut."
The image after I applied a "spiral cut." | Source
Then, in the same folder, I selected “unspiral.”  You’d think that it would straighten the fractal out, but it actually does more to “spiral” it than anything.
Then, in the same folder, I selected “unspiral.” You’d think that it would straighten the fractal out, but it actually does more to “spiral” it than anything. | Source
Taking out the “unspiral” filter and adding “crazy spiral” adds an unexpected element.
Taking out the “unspiral” filter and adding “crazy spiral” adds an unexpected element. | Source
Tweaking the image further and adding a “mirror” filter changes the image still: That’s an image that I like!
Tweaking the image further and adding a “mirror” filter changes the image still: That’s an image that I like! | Source

If I want to further manipulate my image, I can “export” it. That will allow me to make any other changes that I want in GIMP.

So, I can pretend I’m a mathematical genius, but what I really love is the stunning digital images that I can make and manipulate to create a work of art.

I like this image, so I don't think I'll further manipulate it.  I call it "Spinning Spines."
I like this image, so I don't think I'll further manipulate it. I call it "Spinning Spines." | Source

I have become so inspired by these that I created a store and a blog. Every day, I have to spend time making fractals and rendering images that I find graphically and visually stimulating. It's become a sort of...obsession.

So thanks, Movie Master. You helped inspire a new art form for me. I can’t thank you enough.

I'll conclude with some other images I've created.

Click thumbnail to view full-size
This is called "Glory Daze.""Ocean Diatoms""Crowned Jewel""Odyssey""Symbolic Fissure""Wings""Colors in Geode""Dactyl Fractyl""Enigma""Stripe Time""Fantasialand""Rainbow Night""Space Cadet""Spice and Spiral""Spider Lily"
This is called "Glory Daze."
This is called "Glory Daze." | Source
"Ocean Diatoms"
"Ocean Diatoms" | Source
"Crowned Jewel"
"Crowned Jewel" | Source
"Odyssey"
"Odyssey" | Source
"Symbolic Fissure"
"Symbolic Fissure" | Source
"Wings"
"Wings" | Source
"Colors in Geode"
"Colors in Geode" | Source
"Dactyl Fractyl"
"Dactyl Fractyl" | Source
"Enigma"
"Enigma" | Source
"Stripe Time"
"Stripe Time" | Source
"Fantasialand"
"Fantasialand" | Source
"Rainbow Night"
"Rainbow Night" | Source
"Space Cadet"
"Space Cadet" | Source
"Spice and Spiral"
"Spice and Spiral" | Source
"Spider Lily"
"Spider Lily" | Source

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© 2012 Cynthia Calhoun

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