Logistic Map Bifurcation

xn+1 = r · xn(1 − xn) — chaos from simplicity
Click and drag to zoom into a region. Scroll to zoom.
Iterations (skip)

500
Iterations (plot)

200
The logistic map models population growth. As r increases, stable fixed points bifurcate into period-2, period-4, period-8... cycles in a cascade governed by the Feigenbaum constant δ ≈ 4.669 — universal across all period-doubling routes to chaos. Zoom in with mouse drag to reveal infinite fractal self-similarity.