The Edge Effect - Mandelbrot/The Police
This is a really important and not just so psychedelic clip - and it has to do with something you should know about. Take a complex function zn+1 = zn2 + c - where you get the zeroth term starting point at zero. So iterating through - if you start with zero, zero squared gives you the next term z1 = c, and then the second term comes from the previous, third the second, and so on. At the zero, you've got the constant making it go to out to space otherwize, if c=0, then you would just have zero. Fun things happen when you have numbers on the edge of a boundary. Fun places on a planet or at the edge of a star or other places in the universe where guns, germs and steel can give us iron and wine and such great heights.
There are three cases, runaway, center and edge. Say the center. Pretend you're on the edge of a black hole. Go in to close towards the zero, and things collapse in - 1/2, 1/4, 1/16, etc. limit down to zero.
Ok, so go away from the edge. What do you get? You get. Kind of. 2 , 4, 16, 256, etc. Infinity. This clip is a clip of the Mandelbrot Set.
And its a bounded function, which means for some values, cool things happen. Not too far out into space or too far down into the zero but perhaps right along a boundary. This is what this clip is all about, its just a simple set of values, graphed out. The color of the pixel we paint is set by how long it takes to settle down to a value. So what do you think would happen if you surfed the edge?
The application is Fractint, which is freely downloadable. It is being written and maintained by the stone soup group. If you find a good version, please put it up on your website so it can be mirrored. I noticed the original homepage for this app is kind of broken at time of writing. If its still broken by next week, I'll mirror the site myself.