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.
a1.400
b0.300
speed6
WHAT TO TRY
- Watch the orbit stipple in the attractor: zoom in mentally and each smooth band splits into more bands, the Cantor-set cross-section of a strange attractor.
- Drag a between 0.9 and 1.4 and follow the gold dot on the Lyapunov plot: it climbs above zero into chaos, but drops into the deep periodic windows where the orbit collapses onto a finite cycle.
- Lower b toward 0 and the attractor flattens toward the 1D logistic map; the whole Lyapunov curve recomputes for the new dissipation.