Feigenbaum Tree

Period-doubling route to chaos — xₙ₊₁ = r·xₙ·(1−xₙ)

Feigenbaum constants: δ ≈ 4.66920 (ratio of parameter intervals)  |  α ≈ 2.50290 (ratio of orbit widths)
Period-doubling cascade: 1 → 2 → 4 → 8 → … → chaos at r∞ ≈ 3.56995
Orbit time series (selected r)
Cobweb diagram