LOGISTIC MAP — FEIGENBAUM UNIVERSALITY

CONTROLS

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.

Drag the bifurcation diagram to zoom into period-doubling cascades and find the Feigenbaum structure.