Make Your Own Fractals for Fun and Profit!

Well, maybe not for profit, but they are a lot of fun, and it isn’t that difficult to create some beautiful images that will impress your friends.

There are lots of programs that generate fractals, many of which are open source. Fractint is the granddaddy of them all; Apophysis is incredibly powerful but overwhelming in its complexity; Fractal Explorer is very versatile. However, I’m going to focus on just one: Chaoscope, because it’s one of the easiest to use, and beginners can get impressive results. After a few minutes you will be up and running, making beautiful fractal art.

I use it to create desktop wallpapers for my computer, and my students asked where they came from. When I told them that I made them, they begged to learn how. When my students ask me to teach them something, I’m not going to turn them down! Even if you know nothing about the mathematics behind fractals, this can be a really rewarding project for your students. (If you are interested in the math, here are the equations.)

This post is merely a quick introduction to Chaoscope. For a more detailed manual, go here.

Okay, let’s make a fractal!

1. Download the installer file here.

2. After you’ve installed Chaoscope, open it. You will see a very boring blank gray window. Click on “File”, then “New” (or hit Ctrl-N):

File New

 

3. The “New” window should pop up. There are lots of things you can do in this window. First, choose what type of fractal you want to work on (Chaotic Flow, Julia, IFS, Icon, Lorenz, etc.). For your first attempt, I suggest Chaotic Flow:

New

 

In this window, you can also set the dimensions of your fractal. I recommend keeping it relatively small, since the smaller they are, the faster they render. Once you get your fractal exactly the way you like, you can change the size to whatever final dimensions you desire.

4. You can also set the render style in this window. Different styles look, well, different. Gas and Liquid are grayscale, while the others are in color. Solid makes your fractal look like a solid object, and you can also change the background color. I recommend you choose Plasma for this first project.

Render

5. We’re still not seeing any fractal, so let’s have Chaoscope generate one for us. Click the “OK” button in the “New” window. Click on the “Attractor” menu, then choose “Search” (or hit F3):

Attractor

 

You should now see a preview window, a “View” window, and an “Attractor” window. You may have something interesting in your preview window, or you may not. If not, just hit F3 until you get a fractal that looks promising. You can click on the fractal and rotate it in any direction. Often, a fractal that initially seems boring can turn into a spectacular one just by changing the viewing perspective. Here are two different views of the same fractal:

Perspective2

 

 

6. Try tweaking the sliders in the “Attractor” window. You will see that a very small adjustment can have a huge effect. Hitting Ctrl-R will put a random color gradient in place. Right-clicking on the color gradients in the “View” window accesses different gradient maps.

7. If you prefer fractals with lots of symmetry, play with Icon attractors. Lorenz attractors have the famous “butterfly” pattern. Julia attractors have a knobby, organic look.

8. When your fractal is perfect, save the parameters. Then set the size to the desired width and height in the “View” window. Hit the F4 button to have Chaoscope create a high-quality rendering. When it’s done, go to “File” and choose “Save Image As…” to save a bmp file of your masterpiece.

I run Windows 8.1 on my tablet, which allows me to set up a slide show to display a collection of desktop wallpapers. Simply right-click in an open area of your desktop, choose “Personalize”, and create your own theme.

Congratulations! You are now a fractal artist!

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