Monday, 13 September 2010

day 10: She’s Back!

[caption id="attachment_311" align="alignnone" width="300" caption="She's back!"]She's back![/caption]

What is so butter about these flies anyway?

Follow the link by clicking the picture, wait for the applet to load and hit the start button on the page. Now the applet window pops up. Fill in the applet as shown (just the dX0 box), hit Reset and then Start, speed it up by moving the slider.

This is the butterfly attractor of the Lorenz system for two different initial conditions. The amount by which the initial conditions differ is in this case 0.0001, what you filled in at dX0, but you can make it even smaller: 0.0000000001

[caption id="attachment_312" align="alignnone" width="407" caption="Lorenz attractor applet"]Lorenz attractor applet[/caption]

After a while the trajectories start to diverge. At some point both trajectories predict the complete opposite atmospheric conditions. Each coordinate (x,y,z) corresponds to a state of the atmosphere and hence the weather. Imagine that the left wing represents predominantly sunny weather, the right wing could be a nasty hurricane and this difference is “caused” by the very small difference in initial conditions at dX0. It could represent a sneezing butterfly, so small. At least the speech was a storm in glass of water at the other side of the globe.

Must have been my Grog.

It’s apparently a difficult question, about the flying butter.

Chaos is much easier.

Huhuh... He said: “that which gapes wide open, is vast and empty”



Gape-Gaap-Looks random, but probably is not...