Mastering the Logistic Map with Staircase Diagrams 📊

There are a number of tools available to understand discrete-time dynamical systems (or "maps"). In 1-d, one of the best of these is the "staircase diagram" that plot time-(n+1) versus time-(n) points in the plane. The logistic map (an inverted parabola) shows of most of the available dynamical features, from stable and unstable equilibria, to periodic orbits, bifurcation sequences, and chaos.