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]
https://doi.org/10.1016/0167-2789(84)90282-3. Strange attractors that are not chaotic, Physica D 13 (1984), pages 261–268
