While browsing Apple’s website for various openly available math related downloads, I came across JAME, the Java Real-Time Multi-Threaded Fractal Platform. It’s awesome. The JAME website provides the following description:

JAME is a Java real-time, multi-threaded fractal graphics platform which supports images and animations. The core of JAME is the graphics engine which supports layers, filters, effects and alpha composition. JAME creates Mandelbrot and Julia fractals and supports zoom, rotation and colours shifting.

The software is entirely free (under GPL3) and is available for Windows, Mac OS X, and Linux as long as you have met some minimum memory requirements and have an up-to-date version of the Java Runtime Environment installed. The website for the project contains some wonderful tutorials to help get you started, and your creations are exportable to various photo and movie extensions. I created the following clip entirely with JAME:

Now, the rendering of this clip took a while on my Macbook Pro, so if you start playing around keep in mind that the rendering of various movie clips could take a significant amount of time, especially if you increase the frame rate, etc. But the clip above took about 5 minutes to create minus the rendering time. That’s pretty awesome for out of the box capability, let alone all of the customizations that are possible once you learn more about the environment.

There’s a gallery of photos on the site to give you an idea of what’s possible to create more a more advanced user, and some awesome photos have been bundled together into a book that can be purchased here. I’ve seen various movies online that show fractal exploration, but it’s a whole other thing entirely to be in control of the exploration. If you have any interest at all in fractals or mathematical art, I highly suggest checking out the software.

Fractals are beautiful things. If you don’t know what a fractal is, you should read this for a general overview. The most famous fractal (and one of the most mathematically simple) is the Mandelbrot Set, which is named after its discoverer Benoit Mandelbrot. For awhile I’ve wanted to include some sort of video of the Mandelbrot Set “in action”. The following video shows what happens when you “zoom in” on a portion of this fractal. It’s quite interesting. Suffice is it to say that if I ever fall into a bottomless pit, I hope that bottomless pit is like falling into the Mandelbrot Set. At least that way there would be good stuff to look at. There are several other videos out there on the web that show other perspectives of zooming into this particular fractal, so if you like what you see here head over to YouTube or what not and search for some more! The math rock song in the video was written by Jonathan Coulton. If you listen to the lyrics they actually explain a little bit about how to graph this particular fractal. Check out his website here. [Warning: For those of you with sensitive ears, the song that accompanies the video has a few curse words scattered throughout!]