Lorenz system

\begin{align} \dot{x} &= \sigma(y-x)\\ \dot{y} &= x(\rho-z)-y\\ \dot{z} &= xy-\beta z \end{align} using $\beta=8/3$ and $\sigma=10$

fixed points: \begin{align} \mathbf{v}_\text{o} &= (0,0,0)\\ \mathbf{v}_{1,2} &= \left(\pm\sqrt{\beta(\rho-1)},\pm\sqrt{\beta(\rho-1)},\rho-1\right) \end{align}
time $t = $0.00
$\rho=$
written by Hendrik Wernecke