A world in dk(decay/denmark)

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.

Last year I heard about the Critical art Ensemble at digitalfetival. They make concept art which is a genre that I have a very ambivalent relation to. On one hand some of it is just weird and far out for the sake of be weird and far out, and then there are gems, Critical Art Ensemble is one of the fine gems.

The stuff they make are relevant, questioning and thoughtprovoking. As with other concept art – it not the installation at the exhibit thats the most intriguing – but the questions it raises. At their website there are description of some of there works – enjoy www.critical-art.net

Besides Seeing the exhibition of “marching plague” I had the luck to hear Steven Kurtz speak, about Critcal Art Ensembles art and the current case. Because at the moment Steve Kurtz from the Critical Art Ensemble are facing criminal charges, they story is hard to believe – I mean that that this could happen, being charged for for making art. Heres the short introduction from The Critical Art Ensemble Defense fund.

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