Proposed in 1976 by Otto Rössler as a simpler analogue of the Lorenz system, the Rössler attractor requires only one quadratic nonlinearity yet produces full deterministic chaos — an infinite spiral that never retraces itself.
Three differential equations (ẋ = −y−z, ẏ = x+ay, ż = b+z(x−c)) generate the attractor. For a = 0.2, b = 0.2, c = 5.7 the system is chaotic. The attractor has a characteristic band-shaped topology different from Lorenz's double-lobed butterfly.
Rotate the 3D attractor by dragging. Adjust parameters a, b, c to move through period-doubling to chaos. Launch multiple trajectories from nearby points to watch exponential divergence — the hallmark of chaos.
Rössler designed the system while studying chemical reaction oscillators. It later appeared in models of cardiac arrhythmia and the circadian clock. The Rössler band is topologically equivalent to a Möbius strip — one-sided and non-orientable.