Tool

Lyapunov exponent chart

For each value of the control parameter, this tool iterates the chosen map for 1500 steps after a burn-in and averages log|f′(x_n)|. Positive values mean chaos.

λ(r) = lim_{N→∞} (1/N) Σ_{i=0}^{N−1} log |f'(x_i)|

orange segments: λ > 0  →  chaotic
grey segments:   λ ≤ 0  →  stable periodic