Chaotic Maps — Tent & Logistic

Two canonical 1D chaotic maps. Period-doubling route to chaos, bifurcation diagrams, Lyapunov exponents. Click a bifurcation diagram to set r and watch the orbit.

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Tent r = 1.8 Logistic r = 3.7 Initial x₀ = 0.40

Tent λ: —

Logistic λ: —

Tent period: —

Logistic period: —

Tent: f(x) = r·min(x, 1−x)
Logistic: f(x) = r·x·(1−x)

Lyapunov λ = lim(1/N)Σln|f'|
λ > 0 → chaos
λ = 0 → bifurcation point
λ < 0 → stable cycle

Period doublings at
r₁=3, r₂=3.449, r₃=3.544...
Feigenbaum δ = 4.6692...