The logistic map xn+1 = r·xn(1 − xn) captures the entire route from stability to chaos in a single equation. As r increases, fixed points split into cycles that double and double until determinism dissolves into apparent randomness — and yet, windows of order persist.
Feigenbaum constant: δ ≈ 4.669201609... — the universal ratio of successive period-doubling intervals
Drag to zoom · Double-click to reset
The bifurcation diagram reveals how stable equilibria split into oscillations, then chaos, as the parameter r increases. Click on the diagram to select an r value for the cobweb and time series views.