Logistic map

How does a simple map's long-term behaviour depend on its growth rate — and how chaotic does it get?

How the lab tests it

Plot the attractor at every growth rate r (the bifurcation diagram) and measure the Lyapunov exponent λ(r) beneath it.

What it checks

the universal Feigenbaum constant 4.669, λ(4) = ln 2, and chaos onset at r∞ ≈ 3.5699