Archive for October, 2011


TopOc is occupying Durham, for great win and/or lulz! One highlight on the horizon is a leet haxor skillshare – I want to show off the sweet alcohol stove I built! (via this video)

In the meantime, enjoy this pleasing image :)

Praying mantis.... or preying mantis??? Clearly the tyrannosaur of the insect world. Photo via Ildar Sagdejev; clix four phool.

Yay!

cnfusin rained and chas

Last time, we looked at a very simple atmospheric model known as the Lorenz equations, and saw it exhibit the ‘Butterfly Effect,’ in which even very small changes in initial conditions can dramatically effect which path the system takes. However, we also saw that the initial condition had a relatively small impact on the statistical properties of the system. Because climate is a statistical property of the earth system, asking
“How can we expect to predict future climate when we can’t predict the weather?”
is a lot like asking

“How can we claim to know the half-life of a radioactive element when we can’t predict when a given atom will decay?”

To those familiar with chaos, this shouldn’t come as a surprise. Lorenz didn’t just discover apparent disorder in his model, but a deeper, eerie structure lurking in the noise.

The Lorenz Attractor: wibbly-wobbly mess of the millenium. Three simulation runs (red, green, blue) are shown; they start close together but quickly spin off on different trajectories, demonstrating sensitivity to initial conditions. Nonetheless, the trajectories quickly converge on an intricate structure in the phase space, called an 'attractor'. The attractor doesn't vary with initial conditions, but is instead a feature of the Lorenz equations themselves. Image generated with code from TitanLab - click to check them out :)

You may remember that the Lorenz equations relate three variables (X, Y, Z), which vary over time. In the above image, I’ve plotted the evolution of three runs of the Lorenz model by putting a dot at each (X(t), Y(t), Z(t)) coordinate, at every time t in the given interval. The three runs start very close together in this three-dimensional ‘phase space’, but quickly diverge.

However, despite their different individual behaviors, these runs are confined to a structure in phase space, known as the Lorenz attractor – an attractor, because all trajectories converge on it, regardless of their initial conditions. If you perturb the system by bouncing it off the attractor, it quickly settles back into the same loops through phase space. Lorenz (1963) described it: Continue reading

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