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!

2013 Winterim: Fantastic Fractals

I had a small but talented group of students in my Fractals & Chaos mini-course this year. They used Fractal Explorer, Apophysis, Winfeed, and Chaoscope to create their final projects, which are displayed below. Enjoy!


(Equations + Fractals)(Dance) = Beauty

We have a very impressive dance program at Harpeth Hall with amazingly creative choreographers. One of them asked me to create an animation involving equations and fractal animation that will be projected behind some dancers as they perform. The music is a portion of a minimalist piece called “Sextet”, composed by Chris Fitkin, and performed by Piano Circus (available here.)

After four nights of work with Chaoscope and putting my laptop through its paces calculating over 2800 images to create a relatively smooth animation, here is the finished product. I can’t wait to see it all come together on the stage in a couple of months. By the way, pay attention to the last equation, which is possibly the most beautiful in all of mathematics.

The Power of Modern Computing

I was introduced to symmetric fractals (icons) by the 1992 book, Symmetry In Chaos, by Michael Field and Martin Golubitsky. In it, they mentioned that the beautiful images contained in the book were rendered with extremely powerful (at the time) computers.

In the book’s appendix, there were BASIC programs that one could enter and run on his or her home computer. I remember downloading QBasic and laboriously entering and debugging them. After I got one to work on my Intel 486 PC, I had to let it run overnight, because it took so long to plot enough points to get a decent image. Even then, they weren’t very high-resolution. Here’s a typical result:

So what’s the point of this post? Well, in the nine intervening years between the publication of the first edition of Symmetry in Chaos and today, both computers and software have increased exponentially in power and ease of use. Yesterday, I used Chaoscope to create and tweak the ocatagonal symmetric icon below. It was rendered in 22 seconds on my Lenovo X61 tablet, at any resolution I wished.

I can’t imagine what computers will be capable of doing nine years from now.