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Logistic Map & Bifurcation

The deceptively simple rule xn+1 = r xn(1−xn) produces steady states, period-doubling cascades, and full chaos as r grows from 0 to 4. Each bifurcation point arrives faster than the last — the ratio converges to Feigenbaum's constant δ ≈ 4.6692. Click anywhere on the bifurcation diagram to seed an orbit and watch the attractor emerge in the bottom panel.

Bifurcation Diagram
Orbit / Time Series
r:
x:
Period:
r range: 2.5 – 4.0

Click to probe orbit  |  Drag to zoom  |  Double-click to reset