$\newcommand{\dd}{\mathrm{d}}$

Above is an animation of a solution to the Lorenz equations, which are:

\[\frac{\dd x}{\dd t}=\sigma(y-x)\] \[\frac{\dd y}{\dd t}=x(\rho-z)-y\] \[\frac{\dd z}{\dd t}=xy-\beta z\]

The animation shows the solution for $\sigma=10,$ $\ \rho=28$ and $\beta=\frac{8}{3}$ and initial conditions of $x_0=0$, $y_0=1$ and $z_0=20$.

The code for the animation can be found here