Strange attractors, the carriers of chaotic dynamics, don't cover closed surfaces. Their dimensionality is no longer integer but broken (fractal).

The figure shows a torus that becomes a strange attractor by unraveling the minor cross section (partial view bottom right). Stretching, folding and squeezing makes the surface larger and larger, as with a puff-paste, but the volume of the attractor remains the same. Neighbouring orbits depart from one another explosion-like, the system behaves aperiodically but remains recurrent.

As a consequence of the infinitely deep fine structure of the attractor, the system's motion has no preferred scale and becomes unpredictable. Yet, chaotic dynamics are highly organized and irregular but not random.