Abstraction for calculating the Hénon attractor

The "Hénon attractor" (or "Hénon map") is an iterative function that produces a particular chaotic pattern of behavior, which can be visualized or sonified. An iterative function is a formula that uses its own output as an input variable in its own subsequent calculation. In the case of the Hénon map, the function outputs two values, x and y, which can be considered as the coordinates of a point in two-dimensional Cartesian space. Those two output values are then stored to be used as the x and y variables the next time the function is calculated. The output points, when plotted as a series of points on a graph, display a distinctive shape. The function has two additional variables, a and b, which are parameters that influence the pattern of output, but the aggregate of all the output points invariably conforms to the basic Hénon shape.

This abstraction calculates the x and y values for one such point each time it receives a bang (or any message) in its left inlet. You can see and hear one possible visualization/sonification of the Hénon attractor in a related example called "Using the Hénon attractor".