Strange attractor

Under the geometric convention, a strange attractor is an attracting invariant set with irregular, typically fractal geometry rather than a smooth point, cycle or torus. Geometry and orbit instability are separate properties. A strange nonchaotic attractor can be geometrically strange without positive exponential separation. Some authors build chaos into the term instead, so that convention must be distinguished when using it.

A geometrically irregular attractor need not have chaotic exponential separation of nearby trajectories. Quasiperiodically forced systems provide primary examples in which strangeness and a positive largest Lyapunov exponent do not coincide. Consequently a fractal-looking numerical plot alone cannot establish chaos. ^[ref]