Logistic Map Cobweb

xn+1 = r·xn·(1−xn). Drag the r slider to watch fixed point → period-2 → period-4 cascade → chaos. The bifurcation diagram below shows the Feigenbaum route.

Parameter

3.200
0.500
80

Analysis

r3.200
Period—
Lyapunov λ—
State—

Bifurcation landmarks

r₁ = 3.000 → period 2
r₂ = 3.449 → period 4
r₃ = 3.544 → period 8
r∞= 3.5699… → chaos onset
δ = 4.6692… (Feigenbaum)
Chaos window: r > 3.57
Period-3 window: r ≈ 3.83