Control parameter r
Presets:
Bifurcation diagram
Scroll to zoom, drag to pan, click to choose r.
Vertical dashed line: Feigenbaum point r ≈ 3.570. Blue line: selected r = 3.2000.
Trajectory at r = 3.2000
Iterates x₀ = 0.5 → x₁ → x₂ → … Dashed line marks end of initial transient (first 40 steps).
Feigenbaum constant
Period-doubling bifurcations at r = 3, 3.449…, 3.544… crowd together; the ratio of successive interval widths approaches the universal constant δ ≈ 4.669.
Measuring bifurcation spacings from the logistic map…