So after writing a few labs for my class on generating fractals, I went searching online for some pictures that other people came up with. I found the great video on Google Video. To tell you the truth, I think that the complexity of the Mandelbrot set (which is produced by a very simple iteration process) is just amazing and speaks volumes to what is beautiful in the sciences.
I am always at a loss when students will say they think some subject (such as Mathematics) is beautiful but have no ability to reason why. Maybe it takes a philosopher, in the rough sense, to tell why something is beautiful and only a casual observer to say it is beautiful. I really don't like this reasoning though because it lends to the fact that beauty is only in the eye of the beholder (ie relativism) and not a virtue to attain. But if I ever had to explain what beauty is in Mathematics, I think will most definitely point to the Mandelbrot set.
Anyone can generate parts of the Madelbrot set, its really easy to do. It takes a really bright person to fully comprehend all the reasons for its complexity, I mean its just about connecting all possible Julia sets which represent chaotic pattern studies in dynamics .... =D I guess to me there are few things that can be simple stated and represent so much.