Henon Strange Attractor

The Henon map is the simplest system that builds a strange attractor you can draw by hand: each step stretches and folds the plane via x' = 1 - a x^2 + y, y' = b x. At the canonical a = 1.4, b = 0.3 the iterates settle onto the famous banana-shaped set whose cross-section is a Cantor-like dust, fractal dimension about 1.26, and whose nearby points separate exponentially (maximal Lyapunov exponent about 0.42). The playground iterates the map, scatters the attractor, and reports the live Lyapunov estimate; dragging (a, b) morphs and ultimately destroys the attractor. It is the discrete-time companion to the Lorenz attractor and the cleanest place to see stretch-and-fold chaos.