Hénon

Calculate and display the "Hénon" map / attractor

The map was introduced by Michel Hénon as a simplified model of the Poincaré section of the Lorenz model. It is defined by the following equations:

$$ \large \begin{cases} x_{n+1} = 1 - ax_n^2 + y_n \\ y_{n+1} = bx_n \end{cases} \large $$

Where $$x_n$$ and $$y_n$$ are the coordinates at the nth iteration, and a and b are parameters. The map exhibits chaotic behavior for certain values of a and b, and its strange attractor is a classic example of deterministic chaos.