Logistic Map 2D — Bifurcation Diagram & Cobweb Plot

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Growth rate r: 3.5700 Initial x₀: 0.200 Iterations per column: 400 Skip transients: 300 Zoom into region

Stats

r3.5700

x∞ sample—

Periodchaotic

Lyapunov λ—

Regime—

r range[0, 4]

x_n+1 = r·x_n·(1−x_n). Stable fixed point for r<3; 2-cycle at r=3; cascade of doublings accumulates at r≈3.5699 — onset of chaos. Turn on "Zoom into region" then drag a box on the bifurcation diagram to reveal self-similar Feigenbaum structure, or click anywhere on it to jump r there. λ>0 means sensitive dependence on initial conditions.

r = 3.5700
x = 0.2000
period: chaotic