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Gold = periodic orbit · Purple = upper attractor · Teal = lower attractor.

Cobweb: trajectory in (x, f(x)) space.
Measure: time spent at each x (invariant measure ρ).
Basin: initial conditions coloured by period of eventual orbit.

Green λ < 0 — stable, ordered.
Red λ > 0 — chaotic, sensitive.
λ = 0 marks bifurcation points.
The period-3 window (≈3.828–3.857) appears as a green notch inside the red band.

Uses bisection on the super-stable r (where x = 0.5 is a periodic point of f^(2ⁿ)). More doublings and greater depth converge the ratio toward δ.

Top canvas: bifurcation tree zoomed near r∞.
Table: rₙ and δₙ for each period-doubling.