Video Infoblog: Are there other Chaotic Attractors?

Transcript

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Hello. I recently came across a specific set of equations that draw this

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beautiful twisting shape in space and I wanted to share them with you.

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You may have seen it before. It's called the Lorenz attractor. Edward Lorentz

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wanted to know how air moves around in the atmosphere but he found his

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predictions were really inaccurate in the long term. In the long term, weather

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predictions would change a lot if you were to change the initial conditions of

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the simulation only a little. The Lorenz attractor is an illustration of

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this so-called chaotic behavior. Here's how it works : You take a point in space

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with some initial coordinates. Let's say.. (1, 1, 1). Then you move the point according

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to these three equations. What the equations are saying is "every iteration,

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add dx to the x coordinate, dy to the y coordinate and dz to the z coordinate."

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It turns out that if you put two points really close to each other and run the program,

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they stay together in the beginning but they eventually take completely

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different paths. Here I set 500 closely packed points and programmed in some

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pretty trails. As you can see, they seem to be revolving around two regions

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in space. These regions are called attractors. You can never really predict

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when a point will move from one attractor to another and that's what

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makes it chaotic. I found that there's actually a whole bunch of these

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dynamical systems governed by different differential equations.

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I hope you enjoy.