A Chaoscope Strange Attractor

It’s been a very long time since I posted a fractal, so here’s one I made today with the Chaoscope program. It’s an Unravel attractor, rendered in Light mode at 2,000,000,000 iterations:


Here are the parameters:



Fractals and Kindles

I just can’t help myself. Whenever I get a new gadget, I have to customize it. When my wife and daughters gave me a Kindle four years ago, I was thrilled. It’s a Kindle 3, and it opened to me the amazing world of ebooks. My library now includes collections of G. K. Chesterton, Charles Dickens, Fyodor Dostoyevsky, and Shakespeare. I like the fact that the screen isn’t backlit, so there is no eye strain. It’s a wonderful device that has completely changed the way I purchase and read books.

However, I thought the screensavers that Amazon preloaded on the Kindle were really unattractive, so I tried to replace them with images more to my liking. Easier said than done! I assumed that all I had to do was locate the folder containing the screensaver files and dump my own in there. It turns out Amazon does not want you poking around in there, so that folder is hidden.

Fortunately, after a little research online, I was able to hack into my Kindle and change the screensavers. There are thousands of great images online to choose from (just Google “Kindle screensavers”), and I had a blast exploring them. Then it occurred to me that I could create my own fractal screensavers – all that is necessary is to make sure they are gray-scale images that are 600 by 800 in size.

I decided to use Chaoscope to create my screensavers. (I posted a tutorial on how to use Chaoscope here.) Make sure you render them in either Gas or Liquid mode. My first batch is posted below. They are already correctly sized – just click on a thumbnail to access the full-size image, and then save it to your computer. Enjoy!

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:



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.


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):



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:




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!

A Fractal for Valentine’s Day

With Valentine’s Day coming soon, here’s a quick tutorial on how you can create a heart-shaped fractal using the open-source program Apophysis (download it for free here).

1. After opening Apophysis, click on the Transform Editor button:

Transform Editor

In the Transform Editor, click on the New Blank Flame button:

Blank Flame

The Transform Editor window should look like this:

Editor Window

That red triangle you see is called a transform, and we can create all kinds of different effects by changing the values of the Variations. The window in the upper right lets us see a preview of our fractal.

2. In the Variation pane, set the linear value to 0 and the blur value to 0.5. The color of your fractal in the preview window may be different than the one below, and that is fine:


3. Add another transform on top of Transform 1 by clicking the “Adds a new triangle” button:

New Triangle

4. For Transform 2, set the linear value to 0, and the sinusoidal value to 20:


5. Add another transform, and for this one set the linear value to 0, and the julian value to 0.8:


6. Now we’re going to add our final transform. Click on the “Enable final transform” button. Set the linear value of this transform to 0, and the juliascope value to 1:


7. We’re almost done! In the Transform Editor, click the “Triangle” tab above the Variations tab.Click the “Up” arrow three times, moving the final transform up 0.3 units. You should see a nice heart!


Here’s what mine looks like in the main window now:


8. You may not like the color of your heart, so let’s delve into the Gradient tool and change the color scheme. In the main window, click on the Gradient button:


Now you have a gradient window to play with! Clicking on the down arrow next to the “Preset” menu makes hundreds of different gradients available:


After you find one you like, you can use the Rotate slider to scroll through the colors within that particular gradient. Clicking the down arrow next to “Rotate” opens a menu that allows you to adjust the hue, brightness, etc.


Clicking the “Camera” tab lets you adjust the position of your fractal.

9. Save your masterpiece by clicking File, then Save Parameters…. Apophysis has a somewhat weird filing system. It will create a directory with a .flame suffix, and save your parameters within that directory. This allows you to save different variations of the same basic fractal within one directory.

10. To save your fractal as a graphics file, click the Render button:


This opens up a window with options to change the size of your image, determine the location of the rendered image file, and set the quality (the higher the number the better). Click the Render button on the bottom right, and sit back and wait. It will render your fractal as a png file.

We’ve just scratched the surface of what Apophysis is capable of. For further exploration, go back to the Transform Editor and tweak the values of the variations for each transform. For example, select Transform 3 and play around with the julian value.Click on the Variables tab and tinker with the julian_power value.


Move the transforms around in the editor’s window, and see what happens. Have fun – there are an infinite variety of fractals just waiting for you to create!

Here’s my final version:

2014 Valentine

This post is inspired by one of the excellent tutorials available at mfcreative, a site that is a fantastic resource for learning how to use Apophysis.