Physics / Chaos Theory

BIFURCATION MAP

Explore the logistic map route to chaos, period-doubling cascade, and the Feigenbaum constant.

Bifurcation Control

Current behavior: Stable

Growth Rate (r): 3.0

r (numeric)

Zoom: 1.0×

Iterations (quality)

Color Mode

Cobweb Speed

Key Constants

δ ≈ 4.67

Feigenbaum

0.500

Current x

Period

Logistic Map: xₙ₊₁ = r·xₙ·(1−xₙ)

How to use:
• Drag slider to change r
• Click-drag on diagram to zoom
• Double-click to zoom out
• Hover to see r, x values
• Watch cobweb respond in real-time

Bifurcation Diagram

r: 2.5 → 4.0

stable → chaos

Cobweb Plot

Parabola vs y=x iteration

Time Series (x_n vs n)

First 100 iterations (after 200 transients discarded)