my favorite discrete time dynamical system

Given a point in \mathbb{R}^{3}, the next point is:
x_{n+1} = 2\cos(z_{n}-y_{n})
y_{n+1} = 2\sin(x_{n}-z_{n})
z_{n+1} = 7\cos(y_{n}-x_{n})

You can see a high resolution visualization of this here:
http://owen.maresh.info.nyud.net:8080/vrungle-high.mpg

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