LOGISTIC MAP — FEIGENBAUM UNIVERSALITY
CONTROLS
r range start:
2.5
Zoom width:
1.5
r (single orbit):
3.57
Initial x₀:
0.5
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FEIGENBAUM CONSTANT δ
≈ 4.66920160910...
BIFURCATION POINTS r_n
3, 3.449, 3.544, 3.5644...
CHAOS ONSET r_∞
≈ 3.56995...
Logistic Map:
xₙ₊₁ = r·xₙ·(1−xₙ)
Period doubling bifurcations occur at r_n. The ratio of successive intervals converges to Feigenbaum's δ ≈ 4.6692, universal across all unimodal maps.
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the bifurcation diagram to zoom into period-doubling cascades and find the Feigenbaum structure.