x → rx(1-x) bifurcates to chaos through period-doubling — Feigenbaum's universal constant δ ≈ 4.669
Click on bifurcation diagram to select r value — time series shown below
The logistic map xn+1 = r·xn(1−xn) undergoes a period-doubling cascade as r increases.
Bifurcation points: r1 ≈ 3.0 (period 2), r2 ≈ 3.449 (period 4), r3 ≈ 3.544 (period 8)...
The ratio of successive bifurcation intervals converges to Feigenbaum's constant δ ≈ 4.6692...
This constant is universal — it appears in any smooth unimodal map undergoing period-doubling.