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

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. Drag a box on the bifurcation diagram to zoom and reveal self-similar Feigenbaum structure. λ>0 means sensitive dependence on initial conditions.