Rossler funnel attractor

What you are seeing: a cousin of the Lorenz attractor, written down by Otto Rossler in 1976 as the simplest 3D system that still produces chaos (only one nonlinear term, $z \cdot x$). The trajectory winds outward on a flat spiral, then a single fold throws it back to the centre. Push the control parameter $c$ past about $5.7$ and the spiral grows a strong vertical lobe; the geometry earns its "funnel" name.

The equations are $\dot x = -y - z$, $\dot y = x + a\,y$, $\dot z = b + z\,(x - c)$. The classical parameters are $a = b = 0.2$, $c = 5.7$. Drop $c$ to about $4$ and the attractor folds into a clean period-2 limit cycle; sweep it back up through $4.2$, $5.0$, $5.4$ and watch a period-doubling cascade. $\lambda_1$ in the corner is the running estimate of the largest Lyapunov exponent; it stays positive in the chaotic regime (about $0.07$ at the default parameters) and collapses to zero in the periodic windows.