Logistic Map (Bifurcation Diagram)

A classic demographic model that shows how complex, chaotic behavior can arise from very simple non-linear dynamical equations.
x(n+1) = r * x(n) * (1 - x(n))
The horizontal axis is the growth rate `r` (from 2.5 to 4.0). The vertical axis is the long-term stable population `x`. As `r` increases, the population splits (bifurcates) from a single stable state into 2, then 4, 8, and eventually pure chaos, interspersed with islands of stability.