Archive for the ‘Fractal’ Category.
Strange Attractors are quite pretty.
I made have generated quite some random attractors.
Now I need to find the most beautiful ones, and I need your help!
I have created a voting system, where 3 attractors line up and you select the best one. The votes are then accumulated and and overall top 10 is generated.
Strange Attractor wars
It is heavily inspired by kittenwars.com.
I have been hacking away on this far to long. But expect an article with more details on Strange attractors and probably more features in the “war” application. (like top 100, biggest looser, most victorious etc).
Now just go and make some votes
I the moment I’m taking a course in Numerical Analysis, and here we were of course introduced to the Newton-Raphson method for finding roots. That is the method where, geometrical speaking, we take at tangent line to a function and use that to approximate the root, and keep on doing that until we reach satisfying precision.
Depending on where you start the iteration you get a a different root, and requiring a different amount of iterations. That’s self-evident. The “funny” part is that when searching for complex roots there are areas in the complex plane, where a very small difference in starting point gives different roots, and with remarkable difference in the number of iterations.
This is a plot where each root in the polynomial x^4+2 have been assigned a different color. And each point is colored according to which root a iteration starting here finds.
Now thats the mathematical part of it. Now to the beautiful part or at least more fascinating part. The pattern reapeats it self, as a fractal, when you zoom in.
So i modified my code to zoom in, and i used a diffenrent coloring scheme where i only colored according to the number of iterations taken. This made it possible to generate a video zooming in og showing the rapeating patterns in “nice” colors.
Here a some videos :
4 roots (14.6 mb)
7 roots (50 mb)
Yes I know that its very large files, and maybe i will upload them to google video at a later time for easy viewing and less quality.