Henon Map

The Henon map is a discrete-time dynamical system on the plane, defined by a simple pair of equations in which each new point's coordinates are computed from the previous point using one quadratic term and one linear term, making it one of the simplest possible systems capable of producing chaotic behavior from purely deterministic rules. It was introduced in 1976 by the French astronomer and mathematician Michel Henon as a deliberately simplified model of the Lorenz system, a much more complicated set of differential equations already known to produce chaotic weather-like behavior, with the goal of capturing the same essential dynamics in a system simple enough to analyze directly. For its most commonly studied parameter values, the Henon map produces the Henon attractor, one of the earliest concretely computed examples of a strange attractor, a bounded fractal-like set that orbits approach and wander across chaotically without ever exactly repeating or leaving the set. Because it can be iterated extremely quickly on a computer while still reproducing the qualitative features of far more complex chaotic systems, the Henon map became one of the standard textbook examples used to introduce the theory of chaos and strange attractors.