Logistic Map Explorer

The logistic map from r 2.7 to 4.0, with the bifurcation diagram drawn live as you drag the growth rate.

Math & convertChaosBifurcationLogistic

Drag r through the logistic map x' = r x (1-x) and watch the orbit, the unstable fixed point and the Lyapunov exponent move together. Positive lambda means nearby orbits separate; negative means they collapse. CHAOSLYAPUNOVBIFURCATION

Growth rate r

03.6004

Start x₀

Iterations

Orbit — first 600 iterates

Lyapunov exponent

Mean log |f'(x)|-

Samples averaged-

Attractor min x-

Attractor max x-

Unstable fixed point

x* = 1 - 1/r, the branch that loses stability at r = 3.

Residual |f(x*) - x*|-

|f'(x*)| = |2 - r|-

Head of the orbit-

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