Lorentz Attractor
Here you can play with the system of equations known as the Lorentz Attractor:
\[
\frac{d}{dt}\left[\begin{matrix} x \\ y \\ z \end{matrix}\right]
=\left[\begin{matrix} \sigma(y-x) \\ x(\rho-z)-y \\ xy-\beta z \end{matrix}\right]
\]
More description will (possibly) come later. If not, you are invited to consult
the wikipedia page for a background.