Fractal

For those of you interested in the iPhone, a developer named alpheccar has released an application for the device named Mandelbrot, which is a fractal generation tool of the famous Mandelbrot set. It’s a fantastic little free application that allows the user to zoom in on various pieces of the fractal using the typical touch screen commands of the iPhone. Users are also able to discover Julia sets within the fractal, and to switch back and forth between the Mandelbrot and Julia sets.

Many color palettes are included, and the most recent version (1.3.3) allows for palette animation, which creates a great visual effect. The animation is relatively fast, and can be either automatically or manually set. By selecting manual animation, users have the option of setting a slide bar that controls both the speed and accuracy of animation. It’s also possible to save animations to the photo book on the phone.

It’s a great for education and visual entertainment. I really appreciate that this developer took the time to develop such an application and then to distribute it freely. That’s a great gesture. For those of you with an iPhone, a direct link to the application can be found here.

FYI, the photo from this post was taken within the Mandelbrot application and later exported to my computer. Good stuff. Good job, alpheccar!

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 Benoît 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!]