zondag 17 maart 2013

Science cat goes chaotic

A few years ago, I was surfing the web to learn anything about Schrodinger's cat. The one in the box, nor dead nor alive. After clicking on several wikipedia pages (as a pre-graduate student is accustomed to do), I came across the following page.

This was not Schrodinger's cat, but another scientist's cat. Vladimir Arnold (1960) used a picture of a cat to show a particular and cool mathematical feature. Why scientists use cats, I don't know, maybe because these creatures have an intrinsic appearance of being wise and distinguished (except when you put them under the shower, then they transform in complete and utter self pity).

The feature he described was a chaotic mapping procedure. He could transform a picture of a cat into  noise (wow, that is useful), and after some time the cat suddenly arose out of the noise in all its glory (it was as if seeing a magician at work). I wanted to see if I could do the same, hide a cat in chaotic noise and get him back. So I obtained the original paper of Arnold and started working on his method.

I, not being a mathematician (or magician), was struggling through the difficult and a bit obscure material. After a few hours I was able to let my cat disappear in noise, however it stayed there and never came back. That night I could not sleep, desperately thinking about my cat and how to get him out of the (now almost becoming the dark and mysterious, and maybe even a bit magical) noise. How did Arnold get his cat out of the noise?

At 3 AM in the night, I stepped out of bed and walked back to my magical setup (well you can argue this, but computer programming feels like doing magic sometimes). The night sky was clear and the moon was lighting up my keyboard. Maybe due to this magical light (or the coffee I had made for myself) I found the reason why my cat would not magically appear from the noise. The result:

First, I was thinking to put music behind this movie, but I think the beauty of the movie speaks for itself. I have put the number of iterations of the process in the top left corner. The cat is ripped appart (sheared) to become noise. A few times the ghost of the cat is turning up in the movie, and in the end the cat is able to reappear in full form.

I am thinking of applications (You may do to, please leave comments ), however I am still not able to think about a good one. But the beauty of this mathematical trick is remarkable, its just magic.

Please try it yourself!

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