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Logistic Map Orbit Diagram

Parameters

x_{n+1} = r·x_n·(1−x_n)
x ∈ [0,1], r ∈ [0,4]
Period-2 bifurcation: r=3.000
Period-4 bifurcation: r=3.449
Period-8 bifurcation: r=3.544
Onset of chaos: r≈3.5699
Period-3 window: r≈3.8284
Feigenbaum δ: 4.66920…
The logistic map models population growth with resource limits. Period-doubling bifurcations follow a universal ratio: δ≈4.6692 (Feigenbaum constant). This universality applies to any unimodal map — the route to chaos is a law of nature. Hover over the bifurcation diagram to see orbit details.