Lorenz Attractor

A kind of chaotic system which stems from a 2D fluid layer being warmed from below and cooled from above.

dx dt=σ(y−x)dy dt=x(ρ−z)−ydz dt=xy−βz.\begin{aligned} & \frac{\mathrm{d} x}{\mathrm{~d} t}=\sigma(y-x) \\ & \frac{\mathrm{d} y}{\mathrm{~d} t}=x(\rho-z)-y \\ & \frac{\mathrm{d} z}{\mathrm{~d} t}=x y-\beta z . \end{aligned}

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We can generate 3 sequences from this system by looking at the three axes.

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