Logistic bifurcation diagram

For each growth rate r, run x ↦ r x (1 − x) for a while and plot where it ends up. One steady value splits into two, then four, eight, faster and faster, until chaos at r ≈ 3.5699. Inside the chaos sit calm windows that repeat the whole picture in miniature.

xₙ₊₁ = r xₙ (1 − xₙ), δ ≈ 4.6692

Diagramme de Verhulst: mathcurve lists it without an entry, so the link goes to Wikipédia